# Oscar Zariski

#686

Most Influential Person Across History

American mathematician

## Oscar Zariski's AcademicInfluence.com Rankings

Oscar Zariskimathematics Degrees

Mathematics

#28

Historical Rank

Algebraic Geometry

#2

Historical Rank

Measure Theory

#478

Historical Rank

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Mathematics

## Why Is Oscar Zariski Influential?

(Suggest an Edit or Addition)According to Wikipedia, Oscar Zariski was a Russian-born American mathematician and one of the most influential algebraic geometers of the 20th century. Education Zariski was born Oscher Zaritsky to a Jewish family and in 1918 studied at the University of Kyiv. He left Kyiv in 1920 to study at the University of Rome where he became a disciple of the Italian school of algebraic geometry, studying with Guido Castelnuovo, Federigo Enriques and Francesco Severi.

## Oscar Zariski's Published Works

### Published Works

- Commutative Algebra, Vol. II. (1959) (877)
- The Theorem of Riemann-Roch for High Multiples of an Effective Divisor on an Algebraic Surface (1962) (325)
- On the Problem of Existence of Algebraic Functions of Two Variables Possessing a Given Branch Curve (1929) (314)
- The Reduction of the Singularities of an Algebraic Surface (1939) (237)
- Commutative Algebra, Vol. I (1959) (229)
- Local Uniformization on Algebraic Varieties (1940) (197)
- Commutative Algebra II (1976) (191)
- Studies in Equisingularity I Equivalent Singularities of Plane Algebroid Curves (1965) (172)
- Equisingular deformations of normal surface singularities, I (1976) (163)
- Commutative Algebra (1958) (148)
- Some open questions in the theory of singularities (1974) (142)
- Reduction of the Singularities of Algebraic Three Dimensional Varieties (1944) (140)
- On the Topology of Algebroid Singularities (1932) (121)
- Polynomial Ideals Defined by Infinitely Near Base Points (1938) (111)
- Studies in Equisingularity II. Equisingularity in Codimension 1 (and Characteristic Zero) (1965) (100)
- ON THE PURITY OF THE BRANCH LOCUS OF ALGEBRAIC FUNCTIONS. (1958) (99)
- The concept of a simple point of an abstract algebraic variety (1947) (91)
- The Topological Discriminant Group of a Riemann Surface of Genus p (1937) (88)
- On the Poincare Group of Rational Plane Curves (1936) (87)
- Foundations of a general theory of birational correspondences (1943) (86)
- On the irregularity of cyclic multiple planes (1931) (86)
- The compactness of the Riemann manifold of an abstract field of algebraic functions (1944) (85)
- Studies in Equisingularity III: Saturation of Local Rings and Equisingularity (1968) (82)
- A Theorem on the Poincare Group of an Algebraic Hypersurface (1937) (76)
- On Castelnuovo's criterion of rationality $p_{a} =P_{2} =0$ of an algebraic surface (1958) (72)
- CHARACTERIZATION OF PLANE ALGEBROID CURVES WHOSE MODULE OF DIFFERENTIALS HAS MAXIMUM TORSION (1966) (71)
- A new proof of Hilbert’s Nullstellensatz (1947) (57)
- Complete Linear Systems on Normal Varieties and a Generalization of a Lemma of Enriques-Severi (1952) (56)
- Pencils on an algebraic variety and a new proof of a theorem of Bertini (1941) (55)
- A Simplified Proof For the Resolution of Singularities of An Algebraic Surface (1942) (54)
- The theorem of Bertini on the variable singular points of a linear system of varieties (1944) (48)
- Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields (1951) (48)
- Dimension-Theoretic Characterization of Maximal Irreducible Algebraic Systems of Plane Nodal Curves of a Given Order n and with a Given Number d of Nodes (1982) (47)
- The Problem of Minimal Models in the Theory of Algebraic Surfaces (1958) (44)
- A fundamental lemma from the theory of holomorphic functions on an algebraic variety (1949) (42)
- Some Results in the Arithmetic Theory of Algebraic Varieties (1939) (41)
- General Theory of Saturation and of Saturated Local Rings II: Saturated Local Rings of Dimension 1 (1971) (36)
- Analytical Irreducibility of Normal Varieties (1948) (36)
- An Introduction to the Theory of Algebraic Surfaces (1958) (33)
- ON THE LINEAR CONNECTION INDEX OF THE ALGEBRAIC SURFACES z = (fx, y). (1929) (31)
- Foundations of a General Theory of Equisingularity on r-Dimensional Algebroid and Algebraic Varieties, of Embedding Dimension r + 1 (1979) (22)
- On equimultiple subvarieties of algebroid hypersurfaces. (1975) (18)
- General Theory of Saturation and of Saturated Local Rings I: Saturation of Complete Local Domains of Dimension One Having Arbitrary Coefficient Fields (of Characteristic Zero) (1971) (16)
- Normal varieties and birational correspondences (1942) (15)
- A Simple Analytical Proof of a Fundamental Property of Birational Transformations. (1949) (14)
- Generalized weight properties of the resultant of $n+1$ polynomials in $n$ indeterminates (1937) (14)
- Topology of curves and surfaces, and special topics in the theory of algebraic varieties (1978) (13)
- Coble on Algebraic Geometry and Theta Functions (1930) (12)
- General Theory of Saturation and of Saturated Local Rings. III. Saturation in Arbitrary Dimension and, in Particular, Saturation of Algebroid Hypersurfaces (1975) (12)
- Scientific report on the second summer institute, several complex variables. Part III. Algebraic sheaf theory (1956) (12)
- SPLITTING OF VALUATIONS IN EXTENSIONS OF LOCAL DOMAINS. (1955) (11)
- A New Proof of the Total Embedded Resolution Theorem for Algebraic Surfaces (Based on the Theory of Quasi-Ordinary Singularities) (1978) (10)
- A fundamental inequality in the theory of extensions of valuations (1957) (10)
- The Resolution of Singularities of an Algebraic Curve (1939) (9)
- Algebraic Varieties Over Ground Fields of Characteristics Zero (1940) (9)
- On the Non-Existence of Curves of Order 8 with 16 Cusps (1931) (8)
- Reducible Exceptional Curves of the First Kind (1935) (8)
- Hilbert’s characteristic function and the arithmetic genus of an algebraic variety (1950) (7)
- Foundations of algebraic geometry and resolution of singularities (1972) (6)
- The Connectedness Theorem for Birational Transformations (1957) (5)
- On Hyperelliptic θ-Functions with Rational Characteristics (1928) (5)
- On a Theorem of Severi (4)
- On the Problem of Irreducibility of the Algebraic System of Irreducible Plane Curves of a Given Order and Having a Given Number of Nodes (1983) (3)
- ON DIFFERENTIALS IN FUNCTION FIELDS. (1961) (3)
- On the Linearity of Pencils of Curves on Algebraic Surfaces (1938) (2)
- ON CASTELNUOVO ’ S CRITERION OF RATIONALITY Ps 0 OF AN ALGEBRAIC SURFACE (2)
- On the Moduli of Algebraic Functions Possessing a Given Monodromie Group (2)
- On a Theorem of Eddington (1932) (2)
- Polynomial and Power Series Rings (1960) (2)
- Addendum to My Paper "Foundations of a General Theory of Equisingularity on r-Dimensional Algebroid and Algebraic Varieties, of Embedding Dimension r + 1" (1980) (2)
- An unpublished reply. (1980) (1)
- Divisorial cycles on a normal projective variety V/k (dim(V)=r≥1) (1969) (1)
- Topological properties of algebraic surfaces (1948) (1)
- Some Results in the Arithmetic Theory of Algebraic Functions of Several Variables. (1937) (1)
- Intersection theory on algebraic surfaces (k algebraically closed) (1969) (1)
- Equisingularity on algebraic varieties (1979) (1)
- Review: André Weil, Foundations of algebraic geometry (1948) (1)
- The Riemann-Roch theorem (1969) (0)
- Adjoint systems and the theory of invariants (1948) (0)
- The Hilbert characteristic function and the arithmetic genus of a variety (1969) (0)
- Branch curves of multiple planes and continuous systems of plane algebraic curves (1948) (0)
- The canonical system on a variety V (1969) (0)
- Book Review: Foundations of algebraic geometry (1948) (0)
- Proof that any birational class of non-singular surfaces satisfies the descending chain condition. (1959) (0)
- Trace of a differential (1969) (0)
- Homogeneous and non-homogeneous point coordinates (1969) (0)
- Coordinate rings of irreducible varieties (1969) (0)
- Simple and double integrals on an algebraic surface (1948) (0)
- On quadrangular 3-webs of straight lines in space (1933) (0)
- The arithemetic genus (1969) (0)
- Contributions to Algebraic Geometry in Honor of Oscar Zariski (1979) (0)
- THE AMERICAN MATHEMATICAL SOCIETY. (0)
- Continuous non-linear systems (1948) (0)
- The arithmetic genus and the generalized theorem of Riemann-Roch (1948) (0)
- MATHEMA TICS: ZARISKI (0)
- Normalization and complete systems (1969) (0)
- Divisors on an arbitrary variety V (1969) (0)
- An Unpublished Reply (1980) (0)
- Theory and Reduction of Singularities (1995) (0)
- A Topological Proof of the Riemann-Roch Theorem on an Algebraic Curve (1936) (0)
- Holomorphic functions and linear systems (1973) (0)
- Linear systems of curves (1948) (0)
- A Remark Concerning the Parametric Representation of an Algebraic Variety (1937) (0)
- Proof of the fundamental lemma (1969) (0)

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## What Schools Are Affiliated With Oscar Zariski?

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