Andrew J. Sommese | Academic Influence

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Andrew J. Sommese

Mathematics

#4027

World Rank

#5804

Historical Rank

#1428

USA Rank

Measure Theory

#1612

World Rank

#1991

Historical Rank

#534

USA Rank

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Mathematics

Andrew J. Sommese's Degrees

PhD Mathematics University of Notre Dame
Masters Mathematics University of Notre Dame
Bachelors Mathematics University of Notre Dame

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Why Is Andrew J. Sommese Influential?

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According to Wikipedia, Andrew John Sommese is an American mathematician, specializing in algebraic geometry. Sommese received in 1969 from Fordham University a bachelor's degree and in 1973 from Princeton University a PhD under Phillip Griffiths with thesis Algebraic properties of the period-mapping. As a postdoc Sommese was from 1973 to 1975 a Gibbs Instructor at Yale University and was for the academic year 1975–1976 at the Institute for Advanced Study. He became at Cornell University in 1975 an assistant professor and at the University of Notre Dame in 1979 an associate professor and in 1983 a full professor. At the University of Notre Dame he was from 1988 to 1992 the chair of the mathematics department and from 1987 to 1992 the co-director of the Center for Applied Mathematics. Since 1994 he is there Duncan Professor for mathematics.

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Andrew J. Sommese's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The numerical solution of systems of polynomials - arising in engineering and science (2005) (859)
Basic Algebraic Geometry (2005) (713)
The Adjunction Theory of Complex Projective Varieties (1995) (452)
Numerically Solving Polynomial Systems with Bertini (2013) (350)
Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics (1990) (206)
Coefficient-parameter polynomial continuation (1989) (204)
A homotopy for solving general polynomial systems that respects m-homogeneous structures (1987) (201)
Vanishing Theorems on Complex Manifolds (1985) (186)
Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages (1992) (177)
Errata: Computing all solutions to polynomial systems using homotopy continuation (1987) (161)
Software for numerical algebraic geometry: a paradigm and progress towards its implementation (2008) (157)
Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components (2000) (156)
On the adjunction mapping (1987) (129)
Adaptive Multiprecision Path Tracking (2008) (121)
Hyperplane sections of projective surfaces I—The adjunction mapping (1979) (115)
Numerical Homotopies to Compute Generic Points on Positive Dimensional Algebraic Sets (1999) (112)
Complex Differential Geometry (1985) (107)
Regeneration homotopies for solving systems of polynomials (2010) (106)
On the adjunction theoretic structure of projective varieties (1986) (103)
On Reider’s method and higher order embeddings (1989) (102)
Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems (2002) (102)
Submanifolds of Abelian varieties to Rebecca (1978) (94)
Finding all isolated solutions to polynomial systems using HOMPACK (1989) (91)
Using Monodromy to Decompose Solution Sets of Polynomial Systems into Irreducible Components (2001) (87)
Advances in Polynomial Continuation for Solving Problems in Kinematics (2004) (83)
On manifolds that cannot be ample divisors (1976) (81)
Introduction to numerical algebraic geometry (2005) (73)
Numerical algebraic geometry and algebraic kinematics (2011) (72)
Witness sets of projections (2010) (72)
Completeness of solutions of Bethe's equations. (2013) (71)
Results on varieties with many lines and their applications to adjunction theory (1992) (67)
A power series method for computing singular solutions to nonlinear analytic systems (1992) (67)
What is numerical algebraic geometry (2017) (65)
Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core (2012) (60)
Finding All Real Points of a Complex Curve (2006) (60)
Some topological aspects of C* actions on compact Kaehler manifolds (1979) (60)
Computing singular solutions to nonlinear analytic systems (1990) (59)
One-dimensional slow invariant manifolds for spatially homogenous reactive systems. (2009) (55)
Computing singular solutions to polynomial systems (1992) (53)
Regenerative cascade homotopies for solving polynomial systems (2011) (51)
A product-decomposition bound for Bezout numbers (1995) (51)
On K-spannedness for projective surfaces (1990) (51)
A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations (2009) (51)
Mechanism mobility and a local dimension test (2011) (50)
On the density of ratios of Chern numbers of algebraic surfaces (1984) (48)
Homotopy groups of pullbacks of varieties (1986) (48)
On the discriminant variety of a projective manifold (1992) (47)
Extension theorems for reductive group actions on compact Kaehler manifolds (1975) (46)
Homotopies for Intersecting Solution Components of Polynomial Systems (2004) (46)
On the minimality of hyperplane sections of projective threefolds. (1981) (45)
Invariant curves for birational surface maps (2005) (45)
Complex subspaces of homogeneous complex manifolds II—Homotopy Results (1982) (42)
Cell decomposition of almost smooth real algebraic surfaces (2013) (42)
A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws (2013) (42)
Algorithm 801: POLSYS_PLP: a partitioned linear product homotopy code for solving polynomial systems of equations (2000) (42)
Numerical Irreducible Decomposition Using PHCpack (2003) (41)
Efficient path tracking methods (2011) (41)
Numerical Irreducible Decomposition using Projections from Points on the Components (2001) (40)
Numerical factorization of multivariate complex polynomials (2004) (39)
Homotopy techniques for tensor decomposition and perfect identifiability (2014) (39)
Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core (2012) (38)
Projective $n$-folds of log-general type. I (1989) (38)
A numerical-symbolic algorithm for computing the multiplicity of a component of an algebraic set (2006) (37)
A three-dimensional steady-state tumor system (2011) (37)
Notes on Embeddings of Blowups (1996) (37)
Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation (2013) (33)
Quotients by C* and SL(2,C) actions (1983) (33)
A bootstrapping approach for computing multiple solutions of differential equations (2014) (33)
Solving Polynomial Systems Equation by Equation (2005) (32)
On the adjunction theoretic classification of polarized varieties. (1992) (32)
Membership tests for images of algebraic sets by linear projections (2013) (32)
Solution of Polynomial Systems Derived from Differential Equations (2005) (31)
On the preservation ofk-very ampleness under adjunction (1993) (30)
Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials (2009) (30)
Threefolds of degree 9 and 10 in P5 (1990) (28)
Singular solutions, repeated roots and completeness for higher-spin chains (2013) (28)
Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry (2013) (27)
Ample vector bundles and branched coverings (1999) (27)
On the Orders of the Automorphism Groups of Certain Projective Manifolds (1981) (26)
Holomorphic vector-fields on compact Kaehler manifolds (1974) (25)
New properties of special varieties arising from adjunction theory (1991) (25)
A Method for Tracking Singular Paths with Application to the Numerical Irreducible Decomposition (2002) (23)
Line bundles for which a projectivized jet bundle is a product (1998) (23)
A vector bundle characterization of pn (1988) (23)
On the rationality of the period mapping (1978) (23)
Stepsize control for adaptive multiprecision path tracking (2008) (22)
Projective surfaces with K-very ample line bundles of degree ≤ 4K + 4 (1994) (21)
KODAIRA DIMENSION OF SUBVARIETIES (1998) (21)
Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity (2015) (20)
Numerical computation of the genus of an irreducible curve within an algebraic set (2011) (20)
Threefolds of non negative Kodaira dimension with sectional genus less than or equal to 15 (1986) (20)
Stepsize control for path tracking (2009) (19)
Ample divisors on normal gorenstein surfaces (1985) (19)
On the theorem of de Franchis (1983) (19)
Some special properties of the adjunction theory for 3-folds in P[5] (1995) (19)
On the adjunction theoretic classification of projective varieties (1991) (19)
An intrinsic homotopy for intersecting algebraic varieties (2004) (19)
Del Pezzo surfaces as hyperplane sections (1997) (18)
Chern numbers of smooth varieties via homotopy continuation and intersection theory (2009) (17)
A Conjecture about Compact Quotients by Tori (1987) (17)
Borel’s fixed point theorem for Kaehler manifolds and an application (1973) (17)
Exceptional Sets and Fiber Products (2008) (16)
Criteria for quasi-projectivity (1975) (16)
Algorithm 931: An algorithm and software for computing multiplicity structures at zeros of nonlinear systems (2013) (16)
On the nonemptiness of the adjoint linear system of a hyperplane section of a threefold. (1989) (15)
Using Cited Half-life to Adjust Download Statistics (2005) (15)
Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets (2014) (15)
Complex subspaces of homogeneous complex manifolds I. Transplanting theorems (1979) (14)
Numerical Computation of the Hilbert Function and Regularity of a Zero Dimensional Scheme (2014) (14)
Concavity theorems (1978) (14)
Quotients by * and (2,) actions (1983) (14)
THE d-VERY AMPLENESS ON A PROJECTIVE SURFACE IN POSITIVE CHARACTERISTIC (1998) (14)
Ample divisors on 3-folds (1982) (13)
Very ampleness of K_X otimes^L^dimX for ample and spanned line bundles L (1989) (13)
Ample and spanned vector bundles of minimal curve genus (1996) (13)
Theorems of Barth-Lefschetz type for complex subspaces of homogeneous complex manifolds. (1977) (13)
A Parallel Endgame (2010) (13)
On the projective normality of the adjunction bundles (1991) (12)
Hilbert curves of polarized varieties (2010) (12)
Numerical computation of the Hilbert function of a zero-scheme (2011) (12)
Ample Vector Bundles and Branched Coverings, II (2002) (12)
Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety (2014) (12)
On the discriminant locus of an ample and spanned line bundle. (1996) (12)
Numerical Algebraic Geometry and Differential Equations (2014) (11)
Algebraic C*-actions and the inverse kinematics of a general 6R manipulator (2010) (11)
Applications of the Ein-Lazarsfeld criterion for spannedness of adjoint bundles (1993) (11)
Very ample vector bundles of curve genus two (2002) (11)
MULTIPLE STABLE STEADY STATES OF A REACTION-DIFFUSION MODEL ON ZEBRAFISH DORSAL-VENTRAL PATTERNING (2010) (11)
On the dimension of the adjoint linear system for threefolds (1995) (11)
Complex Projective Geometry: Threefolds of degree 11 in P5 (1992) (11)
Quotients by C ∗ × C ∗ Actions (1985) (10)
Applying Numerical Algebraic Geometry to Kinematics (2013) (10)
Chern numbers of ample vector bundles on toric surfaces (1999) (10)
Double covers of P n as very ample divisors (1995) (10)
Algorithm 976 (2017) (10)
Basic Numerical Algebraic Geometry (2005) (10)
Compact complex manifolds possessing a line bundle with a trivial jet bundle: To Professor Erich Kxhler (1978) (10)
Cell Cycle Control and Bifurcation for a Free Boundary Problem Modeling Tissue Growth (2013) (9)
Real algebraic spaces (1977) (9)
Discriminant loci of varieties with smooth normalization (2000) (9)
On Computing a Cell Decomposition of a Real Surface Containing Infinitely Many Singularities (2014) (9)
On the structure of 4-folds with a hyperplane section which is a P 1 bundle over a surface that fibres over a curve (1987) (9)
Reducible hyperplane sections I (1999) (9)
On higher order embeddings of Fano threefolds by the anticanonical linear system (1997) (8)
On generation of jets for vector bundles (1999) (8)
Algorithms in algebraic geometry (2008) (8)
Quaternionic manifolds (1975) (8)
Algorithm 976: Bertini_real: Numerical Decomposition of Real Algebraic Curves and Surfaces (2017) (7)
Quotients by *×* actions (1985) (7)
On the Minimality of Hyperplane Sections of Gorenstein Threefolds (1986) (7)
On the Dimension of the Adjoint Linear System for Quadric Fibrations (1994) (7)
A criterion for a variety to be a cone (1987) (7)
Vibrations of thin plates with small clamped patches (2015) (6)
Projections from Subvarieties (1998) (6)
Addendum to “criteria for quasi-projectivity” (1976) (6)
Some Algebraic Properties of the Image of the Period Mapping (1973) (6)
On blowing down projective spaces in singular varieties. (1985) (6)
Algebraic properties of the period mapping (1973) (6)
Piecewise Linear Approximation of Smooth Compact Fibers (2002) (6)
SL(2, C) Actions on Compact Kaehler Manifolds (1983) (6)
A generalization of a theorem of Horrocks (1982) (6)
A LOCAL DIMENSION TEST FOR NUMERICALLY APPROXIMATED POINTS ON ALGEBRAIC SETS (2008) (6)
Non-smoothable varieties (1979) (6)
Classification of irreducible projective surfaces of smooth sectional genus $\leqq 3$. (1990) (5)
Errata: Coefficient-parameter polynomial continuation (1992) (5)
Numerical Local Irreducible Decomposition (2015) (5)
Review: Kunihiko Kodaira, Complex manifolds and deformation of complex structures (1987) (5)
Notes on very ample vector bundles on 3-folds (2005) (5)
Ample vector bundles with zero loci having a hyperelliptic curve section (2003) (5)
Homotopies for Connected Components of Algebraic Sets with Application to Computing Critical Sets (2017) (5)
BIFURCATION OF STEADY-STATE SOLUTIONS FOR A TUMOR MODEL WITH A NECROTIC CORE (2010) (5)
Multiprecision path tracking (2006) (5)
On the second adjunction mapping. The case of a 1-dimensional image (1997) (5)
On generically polarized Gorenstein surfaces of sectional genus two. (1988) (5)
On the projective classification of smoothn-folds withn even (1989) (4)
Singular Value Decomposition of Complexes (2018) (4)
Some examples of ℂ* actions (1982) (4)
Filtrations of meromorphic $C^*$ actions on complex manifolds. (1983) (4)
Reducible hyperplane sections, II. (2002) (4)
On the nonemptiness of the adjoint linear system of a hyperplane section of a threefold. (1989) (4)
Special results in adjunction theory in dimension four and five (1993) (4)
Varieties whose hyperplane section are $\mathbb {P}_\mathbb {C}^{\,k}$ bundles (1988) (4)
A NOTE ON P 1 -BUNDLES AS HYPERPLANE SECTIONS (2005) (4)
Chern Inequalities and Spannedness of the Adjoint Bundle (1996) (4)
Mathematical reduction of a heart dipole model (1989) (4)
Closure to “Discussion of ‘Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages’” (1997, ASME J. Mech. Des., 119, pp. 149–150) (1997) (3)
NUMERICAL COMPUTATION OF THE DIMENSIONS OF THE COHOMOLOGY OF TWISTS OF IDEAL SHEAVES (2008) (3)
On the degree of the Gauss mapping of a submanifold of an Abelian variety (1984) (3)
A remark on the Kawamata rationality theorem (1993) (3)
ON THE DEGREE AND THE BIRATIONALITY OF THE SECOND ADJUNCTION MAPPING (1999) (3)
Perturbation results on the zero-locus of a polynomial (2017) (3)
Application of a Numerical Version of Terr Acini’s Lemma for Secants and Joins (2008) (3)
On the Adjunction Mapping for Singular Projective Varieties (1989) (3)
Bertini real : Numerical Decomposition of Real Algebraic Curves and Surfaces (2015) (3)
A NOTE ON P1-BUNDLES AS HYPERPLANE SECTIONS (2005) (2)
Adjunction and singular loci of hyperplane sections (2015) (2)
PROJECTIVE MANIFOLDS WITH SMALL PLURIDEGREES (1999) (2)
Generic properties of the adjuction mapping for singular surfaces and applications (1990) (2)
Reversing the Ahlfors’ estimate (1974) (2)
What we know about the second adjunction mapping (1997) (2)
Mathematical Software – ICMS 2016 (2016) (2)
Two results on branched coverings of Grassmannians (1998) (2)
Algorithms in Algebraic Geometry (The IMA Volumes in Mathematics and its Applications) (2007) (2)
A domain decomposition algorithm for computing multiple steady states of differential equations (2011) (2)
Higher dimensional polarized varieties with non-integral nefvalue (2003) (2)
Classification of algebraic varieties : Algebraic Geometry Conference on Classification of Algebraic Varieties, May 22-30, 1992, University of L'Aquila, L'Aquila, Italy (1994) (1)
On the bicanonical map of a surface section of a threefold (2001) (1)
Ideals, Varieties, and Algorithms-An Introduction to Computational Algebraic Geometry and Commutative Algebra (D. Cox, J. Little, and D. O'Shea) (1993) (1)
On the complexity of the projective classification of surfaces (1995) (1)
Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core (2012) (1)
(2,) actions on compact Kaehler manifolds (1983) (1)
On the adjunction mapping of very ample vector bundles of corank one (2003) (1)
Calculation of Slow Invariant Manifolds for Reactive Systems (2009) (1)
QSharp Matsusaka‐Type Theorems on Surfaces (1998) (1)
On the relative adjunction mapping. (1989) (1)
Classification of Algebraic Varieties (1994) (1)
Special Vanishing Theorems (1985) (1)
Polynomial Systems Arising From Discretizing Systems of Nonlinear Differential Equations (2018) (0)
Interactions of classical and numerical algebraic geometry : a conference in honor of Andrew Sommese, Interactions of Classical and Numerical Algebraic Geometry, May 22-24, 2008, University of Notre Dame, Notre Dame, Indiana (2009) (0)
Chapter 12. The second reduction in dimension three (1995) (0)
Generalizations of the Kodaira Vanishing Theorem (1985) (0)
Chapter 8. Background for classical adjunction theory (1995) (0)
Algebraic Geometry: Proceedings of the International Conference, held in L'Aquila, Italy, May 30 - June 4, 1988 (1990) (0)
Vector Bundles: Geometric Positivity (1985) (0)
The Intersection Of Algebraic Sets (2005) (0)
HOMOTOPY GROUPS OF FULLBACKS OF VARIETIES (2004) (0)
Chapter 11. Classical adjunction theory in dimension ≥ 3 (1995) (0)
Chapter 4. The Hilbert scheme and extremal rays (1995) (0)
Number of Real Critical Points of Cyclotomic Polynomials (2019) (0)
Adaptive multiprecision path tracking Daniel J. BatesJonathan D. Hauenstein (2007) (0)
Book Review: Classification theories of polarized varieties (1992) (0)
Generalizations of the Nakano Vanishing Theorem (1985) (0)
Midwest Algebraic Geometry Conference (1997) (0)
The Numerical Irreducible Decomposition (2005) (0)
Chapter 14. Special varieties (1995) (0)
Classical integration rules and Wiener measure (0)
Collapsing the Resultant Dipole System (1987) (0)
Manifolds with Nef Rank 1 Subsheaves in Ω X 1 (2002) (0)
Coefficient-Parameter Homotopy (2005) (0)
Cell Cycle Control and Bifurcation for a Free Boundary Problem Modeling Tissue Growth (2013) (0)
Chapter 1. General background results (1995) (0)
Erratum to "Discriminant loci of varieties with smooth normalization" (2003) (0)
Constructing Slow Invariant Manifolds for Reactive Systems with Detailed Kinetics (2008) (0)
A Cascade Algorithm for Witness Supersets (2005) (0)
Projective Space Method for Slow Invariant Manifolds of Reactive Systems (2009) (0)
Quotients by C* X C* Actions Let X Be a Connected Compact Kahler Manifold with a Meromorphic Action of F« (c*)k (2010) (0)
Chapter 5. Restrictions imposed by ample divisors (1995) (0)
Adjunction and singular loci of hyperplane sections, II (2014) (0)
Quotients by ${\bf C}\sp\ast \times{\bf C}\sp\ast$ actions (1985) (0)
Adjunction and singular loci of hyperplane sections, II (2014) (0)
Real Numerical Algebraic Geometry: Finding All Real Solutions of a Polynomial System (2014) (0)
Chapter 2. Consequences of positivity (1995) (0)
Chapter 3. The basic varieties of adjunction theory (1995) (0)
A pr 1 99 8 Projections from Subvarieties (1998) (0)
Duties and Powers The Academic Council • Authorizes establishment or discontinuance ' of academic organizations • Considers recommendations of Graduate Council • Sets academic policy • Approves major changes in admissions requirements Council to deliberate issues of harrassment , academics (0)
On the Relation Between Reaction Dynamics and Thermodynamics in Closed Systems (2009) (0)
Genericity and Probability One (2005) (0)
Quotients by ${\bf C}\sp{\ast} $ and ${\rm SL}(2,{\bf C})$ actions (1983) (0)
Vector Bundles: Ampleness (1985) (0)
Chapter 9. The adjunction mapping (1995) (0)
University of Birmingham Exercising Nuprl's open-endedness (2016) (0)
Cell decomposition of almost smooth real algebraic surfaces (2012) (0)
Chapter 10. Classical adjunction theory of surfaces (1995) (0)
Polynomials of One Variable (2005) (0)
A representable functor theorem for compact analytic spaces and applications (1975) (0)
On the projective classification of smooth<Emphasis Type="Italic">n</Emphasis>-folds with<Emphasis Type="Italic">n</Emphasis> even (2006) (0)
Checking Results and Other Implementation Tips (2005) (0)
Algorithm xxx: Bertini real: Numerical Decomposition of Real Algebraic Curves and Surfaces (2017) (0)
A Chebyshev method for a free boundary problem modeling tumor growth (2013) (0)
Chapter 13. Varieties (ℳ, ℒ) with k(ΚΜ + (dim ℳ - 2)ℒ)≥0 (1995) (0)
Numerical Algebraic Geometry: Theory and Practice (2014) (0)
Applications of Numerical Terracini ’ s Lemma (2006) (0)
Almost homogeneous C* actions on compact complex surfaces (1982) (0)
Kodaira-Nakano Vanishing Theorems (1985) (0)
Chapter 7. General adjunction theory (1995) (0)
Numerical irreducible decomposition over a number field (2017) (0)
Correction to "$\mathsf{C}^*$-actions". (1983) (0)
Pacific Journal of Mathematics the D-very Ampleness on a Projective Surface in Positive Characteristic Hiroyuki Terakawa (2007) (0)
Chapter 6. Families of unbreakable rational curves (1995) (0)
Complexity of Integration, Special Values, and Recent Developments (2016) (0)
Efficient endgames and path tracking methods (2009) (0)

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