Shigeru Mukai

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Shigeru Mukai is affiliated with the following schools: University of California, Los Angeles, Nagoya University, Kyoto University

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Shigeru Mukai

Mathematics

#2915

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#4396

Historical Rank

Measure Theory

#1337

World Rank

#1684

Historical Rank

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Mathematics

Shigeru Mukai's Degrees

PhD Mathematics Kyoto University

Why Is Shigeru Mukai Influential?

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According to Wikipedia, is a Japanese mathematician at Kyoto University specializing in algebraic geometry. Work He introduced the Fourier–Mukai transform in 1981 in a paper on abelian varieties, which also made up his doctoral thesis. His research since has included work on vector bundles on K3 surfaces, three-dimensional Fano varieties, moduli theory, and non-commutative Brill-Noether theory. He also found a new counterexample to Hilbert's 14th problem .

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Shigeru Mukai'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

Symplectic structure of the moduli space of sheaves on an abelian or K3 surface (1984) (681)
Duality between D(X) and with its application to picard sheaves (1981) (404)
Finite groups of automorphisms of K3 surfaces and the Mathieur group (1988) (320)
Classification of Fano 3-folds with B2≥2 (1981) (308)
Biregular classification of Fano 3-folds and Fano manifolds of coindex 3. (1989) (252)
An Introduction to Invariants and Moduli (2003) (245)
The uniruledness of the moduli space of curves of genus 11 (1983) (242)
Curves, K3 Surfaces and Fano 3-folds of Genus ≤ 10 (1988) (210)
Classification of Fano 3-folds with B2≥2 (1981) (210)
Semi-homogeneous vector bundles on an abelian variety (1978) (148)
Curves and symmetric spaces (1995) (142)
Fourier Functor and its Application to the Moduli of Bundles on an Abelian Variety (1987) (122)
Complex Projective Geometry: Fano 3-folds (1992) (119)
Non-Abelian Brill-Noether theory and Fano 3-folds (1997) (68)
Maximal subbundles of vector bundles on a curve (1985) (65)
Counterexamples to Kodaira’s vanishing and Yau’s inequality in positive characteristics (2013) (61)
Automorphisms of Enriques surfaces which act trivially on the cohomology groups (1984) (61)
Geometric Realization Of T -shaped Root Systems and Counterexamples To Hilbert's Fourteenth Problem (2004) (58)
Photoluminescent and electrical properties of InGaPAs mixed crystals liquid phase epitaxially grown on (100) GaAs (1983) (50)
Vector Bundles and Brill{Noether Theory (1995) (47)
Fundamental mode oscillation of a buried ridge waveguide laser array (1984) (47)
Finite generation of the Nagata invariant rings in ADE cases (2005) (47)
Polarized K3 surfaces of genus thirteen (2006) (46)
Doping and electrical properties of Mg in LPE AlxGa1−xAs (1979) (43)
Counterexample to Hilbert''s fourteenth problem for three dimensional additive groups (2001) (42)
Vector Bundles on a K3 Surface (2003) (42)
Complex Projective Geometry: Polarized K3 surfaces of genus 18 and 20 (1992) (41)
Polarized K 3 surfaces of genus 18 and 20 (2009) (40)
Curves and symmetric spaces, II (2010) (38)
Numerically trivial involutions of Kummer type of an Enriques surface (2010) (36)
Simple Lie algebra and Legendre variety (1999) (32)
New Trends in Algebraic Geometry: Duality of polarized K3 surfaces (1999) (29)
Beam scanning and switching characteristics of twin-striped lasers with a reduced stripe spacing (1985) (28)
Optical absorption of Cu-centers in CdCl2 and CdBr2 single crystals (1973) (27)
Heteroepitaxial Growth of GaP on Silicon by Molecular Beam Epitaxy (1978) (27)
MOLECULAR BEAM EPITAXIAL GROWTH OF GaAs. (1975) (26)
On Fano 3-Folds with $B_2\geq 2$ (1983) (23)
Continuous Output Beam Steering in Vertical-Cavity Surface-Emitting Lasers with Two p-Type Electrodes by Controlling Injection Current Profile (1999) (22)
Plane quartics and Fano threefolds of genus twelve (2004) (22)
Vibronically Allowed d-d Transitions of Cu2+ Centers in CdCl2 and CbBr2 (1974) (22)
Optoelectronic fuzzy inference system based on beam-scanning architecture. (1994) (20)
Stability and Einstein-Kähler Metric of a Quartic del Pezzo Surface (2020) (20)
Characterization and Substrate-Temperature Dependence of Crystalline State of GaAs Grown by Molecular Beam Epitaxy (1975) (20)
Molecular Beam Epitaxial Growth of InP (1976) (20)
Laser beam scanning using a local deflector integrated with an effective mode filter (1987) (20)
Optical tristability using a twin‐stripe laser diode (1987) (19)
Abelian variety and spin representation ∗ (1999) (19)
Analysis of mode behavior in a waveguide with graded index and gain (1984) (17)
Transverse junction buried heterostructure (TJ-BH) AlGaAs diode laser (1987) (16)
Surface-emitting laser diode with distributed Bragg reflector and buried heterostructure (1990) (16)
Obstructions to deforming curves on a 3-fold, I: A generalization of Mumford’s example and an application to schemes (2006) (16)
Liquid phase epitaxial growth of AlGaInPAs lattice matched to GaAs (1984) (15)
Low-threshold surface-emitting laser diodes with distributed Bragg reflectors and current blocking layers (1990) (14)
Continuously operated visible‐light‐emitting lasers using liquid‐phase‐epitaxial InGaPAs grown on GaAs substrates (1983) (14)
Moduli Spaces and Arithmetic Geometry (2007) (14)
Finite groups of automorphisms of Enriques surfaces and the Mathieu group $M_{12}$ (2014) (13)
Canonical curves of genus eight (2003) (13)
Kummer's quartics and numerically reflective involutions of Enriques surfaces (2012) (12)
Fundamental Study on the Flotation of Non-Sulfide Minerals Using Two Kinds of Collectors (1978) (12)
Degradation and intensity fluctuations in CW AlGaAs double-heterostructure junction lasers (1975) (12)
LPE Growth and Luminescence of In1-xGaxPyAs1-y on (1, 0, 0) GaAs with Band-Gap Energy in Region of 1.569 eV≤Eg≤1.893 eV (1980) (12)
The automorphism groups of enriques surfaces covered by symmetric quartic surfaces (2015) (12)
Transverse second‐order mode oscillations in a twin‐stripe laser with asymmetric injection currents (1983) (12)
Ultraviolet absorption spectra of metalorganic molecules diluted in hydrogen gas (1988) (11)
K3 surfaces of genus sixteen (2016) (11)
Energy levels of nitrogen isoelectronic impurities in AlxGa1−xAs (1976) (11)
Moduli of abelian surfaces , and regular polyhedral groups (2003) (11)
Fabrication and Visible-Light-Emission Characteristics of Room-Temperature-Operated InGaPAs DH Diode Lasers Grown on GaAs Substrates (1981) (11)
Nitrogen doping into GaAs1−xPx using ionized beam in molecular beam epitaxy (1978) (10)
Zn, Te and Se Doping of LPE InGaPAs0.01 Grown on (100) GaAs Substrates (1982) (10)
Effect of cavity size on lasting characteristics of a distributed Bragg reflector‐surface emitting laser with buried heterostructure (1992) (9)
LPE Growth of In1-xGaxP1-zAsz (z ≦0.01) on (1 0 0) GaAs Substrates and Its Lattice Constants and Photoluminescence (1981) (9)
VA-1 distributed feedback surface emitting laser diode with lateral double heterostructure (1987) (9)
Enriques Surfaces of Hutchinson–Göpel Type and Mathieu Automorphisms (2013) (9)
Trilateral optical powermeter comparison between NIST, NMIJ/AIST, and METAS. (2007) (8)
Influence of carrier spreading on the current‐controlled lateral‐mode behavior of twin‐stripe lasers (1990) (8)
A semiconductor laser with a converging output beam (1985) (7)
Vertical field‐effect transistors in III‐V semiconductors (1984) (7)
Surface Decomposition of GaAs Substrates in LPE Growth of InGaAsP and Its Effect on Crystal Quality (1981) (7)
Use of Multiple Pairs of Gain and Saturable Absorber Regions for Semiconductor Optical-Pulse Compressor (2000) (7)
Optoelectronic implementation of real-time control of an inverted pendulum by fuzzy-logic-control units based on a light-emitting-diode array and a position-sensing device. (1997) (6)
Mutual phase locking of a coupled laser diode‐Gunn diode pair (1984) (6)
Coupled parallel waveguide semiconductor laser (1984) (6)
Electroreflectance and photoluminescence studies of (AlxGa1−x)1−zInzPyAs1−y lattice matched to GaAs (1987) (6)
Analysis of a double-heterostructure spatial-phase controller for diode-laser beam steering (1988) (6)
Local beam deflector interated in a diode laser cavity (1987) (6)
LECTURE NOTES ON K3 AND ENRIQUES SURFACES (2011) (6)
AlGaAs/GaAs buried quantum well laser diodes by one time selective metalorganic chemical vapor deposition growth on dielectric window stripes (1993) (5)
Very low‐threshold separate‐confinement‐heterostructure lasers prepared by liquid phase epitaxy (1985) (5)
Diffusion Properties of Mg in AlxGa1-xAs (1989) (5)
Mechanism of the negative slope in the current‐light characteristics of twin‐stripe lasers (1987) (5)
Temperature dependence of photoluminescence spectra of the pentanary alloy semiconductor (AlxGa1−x)1−zInzPyAs1−y (1988) (5)
Analysis of lateral-mode behavior of twin-stripe lasers related to the negative slope in their current-light characteristics (1988) (4)
Counterexample of Kodaira ’ s vanishing and Yau ’ s inequality in higher dimensional variety of characteristic p > 0 By (2005) (4)
Principles of Sulphide Mineral Flotation (1970) (4)
Final report on APMP.PR-S4: Comparison of fiber optic power meter responsivity (2011) (4)
An LPE Growth Method to Reduce Thermal Degradation of Substrates (1980) (4)
Monolithic integration of a lens inside a diode‐laser cavity for beam convergence (1985) (4)
Analysis of intensity fluctuations in a junction laser with low quantum-efficiency regions (1976) (4)
An active beam-scanning optoelectronic logic gate (1991) (4)
Effects of collector ion concentrations and hydrogen ion concentrations on the floatability of non-sulphide minerals. (1962) (3)
Resultants and the Borcherds Φ-Function (2013) (3)
Vertical FET's in GaAs (1984) (3)
Copper Ion Adsorption on Sphalerites of Various Iron Contents (1970) (3)
LPE Growth and Luminescence of InGaAsP Lattice-Matched to (1, 0, 0) GaAs Substrates (1980) (3)
Raman spectra of the pentanary alloy semiconductor (AlxGa1−x)1−zInzPyAs1−y (1988) (3)
Effect of Degradation on Intensity Fluctuation in cw AlGaAs Double-Heterostructure Junction Lasers (1975) (2)
LPE Growth of AlGaAs-GaAs Quantum Well Heterostructures (1989) (2)
The Effect of Doping on Interface Morphology in LPE AlxGa1-xAs (1977) (2)
Treatment of Waste Water from Chromium Plating by Solvent Extraction (1975) (2)
Desulphurization of Coal with Some Oxidizing Reagents (I) (1969) (2)
Transverse beam deflection in a semiconductor laser (1986) (2)
Effect of structural disorder to photo-electron in pentanary alloy semiconductor AlGaInPAs (1989) (2)
Equations defining a space curve (1999) (2)
Influence of interstripe gain on crosscoupled-mode operation in twin-stripe lasers (1993) (2)
A travelling-wave beam deflector cleave-coupled to a diode laser (1989) (2)
RIMS-1736 COUNTEREXAMPLES OF KODAIRA’S VANISHING AND YAU’S INEQUALITY IN POSITIVE CHARACTERISTICS (2011) (2)
Mutual Action of Amine Collector and Alcohol as a Frother in the Amine Flotation (1978) (1)
Traveling wave spatial phase controller for diode-laser-beam scanning (1988) (1)
Bilateral optical fiber power meter linearity comparison between NMIJ and NIST (2008) (1)
j-invariant and Borcherds Phi-function (2021) (1)
Electrochemical study on flotation. (1962) (1)
Mineral Processing and Refining of Rare Earth Elements (1985) (1)
Buried-heterostructure diode lasers with in-situ-grown self-aligned GaAs mask for Zn diffusion (1987) (1)
Optoelectronic fuzzy inference architecture using beam-steering vertical cavity surface-emitting laser diodes (1999) (1)
Fabrication of buried‐heterostructure diode lasers using in situ Mg diffusion (1989) (1)
Effect of Multi-Stage Crushing on the Size Distribution Control of Crushed Product of Iron Ore (1968) (1)
High-precision linearity standard for high-power optical-fiber power meters (2008) (1)
Optical tristability and associated ternary digital functions using a twin-stripe laser diode (1988) (1)
Nonmonotonic threshold size dependence of buried-post vertical cavity lasers (2001) (1)
Optoelectronic fuzzy logic inference system using beam scanning laser diodes (1993) (1)
Binary logic operations using a beam scanning laser diode (1992) (1)
Finite and infinite generation of the Nagata invariant rings (2005) (1)
Beam Scanning Binary Logic ( OPTICAL COMPUTING 1) (1990) (1)
[A new method of age estimation in dentistry]. (1966) (1)
Observation of switching related to bistability between two cross-coupled lateral modes in twin-stripe lasers (1994) (1)
Resultants and the Borcherds Phi-function (2013) (1)
Hardening of KCl Crystals by FA-Centers (1968) (1)
Wavelength dependence of non-linearity of optical fibre power meters (2011) (1)
Soap Flotation of Barite (1961) (1)
Integration of a diode laser and an electronic lens for controlling the beam focus position (1989) (1)
Study on the Treatment of Industrial waste water by Flotation Method (I) (1969) (1)
Desulfurization of coal with some oxidizing reagents. I. Desulfurization by treatment with chlorine gas and hydrogen peroxide. [Desulfurization at room temperature] (1969) (1)
Optical high-power nonlinearity comparison between the National Institute of Standards and Technology and the National Metrology Institute of Japan at 1480 nm. (2010) (1)
Flotation of bastnaesite from complex ores with anionic collector (1984) (1)
Study on the Removal of Mercury Ion in Waste Water (1973) (1)
Self-routing optical bus and optical link using beam-scanning laser diodes (1993) (0)
Improved Waveguide Laser Array (1986) (0)
An Introduction to Invariants and Moduli: Curves and their Jacobians (2003) (0)
Beam Scanning Binary Logic (1990) (0)
Grassmannians and vector bundles (2000) (0)
Optical Ternary Memory and Logic Operation using a Twin-Stripe Laser Diode (1987) (0)
On the Separation of Pyrrhotite and Sphalerite (1969) (0)
Kyoto Journal of Mathematics: Preface (2010) (0)
Optically-Bistable Devices and Their Application to Infomotion Processing (1987) (0)
The Hilbert scheme of canonical curves in del Pezzo 3-folds and its application to the Hom scheme (2006) (0)
Optical Tristability Using a Twin-Stripe Laser Diode (1986) (0)
A New Analysis of Comminution Processes by Matrix Representation (1966) (0)
On the pH Dependence for the Copper Activation of Sphalerite (1969) (0)
The Action of Oxygen on the Adsorption of Xanthate at the Sulphide Mineral/Water Interface (1971) (0)
Semiconductor lasers with various functions realized by controlling lateral-mode behavior (1992) (0)
Analysis of Modes in a Vertical Cavity Surface Emitting Laser with Multilayer Bragg Reflectors (1994) (0)
An optoelectronic full adder using: a beam scanning laser diode (1992) (0)
Cavity length limitation of the cross-coupled mode bistability in a semiconductor laser (1996) (0)
Biregular classification ofFano3-folds andFanomanifolds of coindex 3 (Grassmann variety/vector bundle/K3 surface/homogeneous (1989) (0)
Quantum Electronics Letters Observation of Switching Related to Bistability Between Two Cross-Coupled Lateral Modes in Twin-S tripe Lasers (1994) (0)
The Work Index of the Iron Ore (1967) (0)
Electrode Factors (Diameter, Clearance and Applied Voltage) and Particle Distribution on Electrostatic Separation (1959) (0)
Stabilisation of fundamental-lateral-mode oscillations using optical feedback within an integrated amplifier/laser array (1991) (0)
Electrostatic Separation of Coal (1969) (0)
Influence of Interfacial Tension and Electronic Charge on Contact Angle in Mercury-Electrolyte Solution System (1960) (0)
Fundamental Study of Non-Sulfide Mineral Flotation Using Dodecylammonium Chloride as a Collector (1975) (0)
Study on the Deactivation of Sphalerite with Acid and Ferric Ion Solutions (1969) (0)
Mechanism of Depressant Action on Flotation of Suphide Minerals (1958) (0)
Workshop: Komplexe Algebraische Geometrie Table of Contents (2005) (0)
Relation among Adsorption of Collector Ion, Change of Electrokinetic Potential and Floatability of Mineral Particles (1959) (0)
Multidimensional optical interconnections using beam‐scanning laser diodes (1992) (0)
Relation between the Size Distribution of Crushed Product and the Rate of Loading for Iron Ore Crushing (1969) (0)
[Relationship among the teeth and factor analysis]. (1978) (0)
Consideration on Liberation of Mineral in Ore (1957) (0)
Study on the Electrostatic Concentration of Low Ash Coal in Corona Field (1962) (0)
The composition of frothers and its influence on the floatability of mineral particles (1976) (0)
The construction of quotient varieties (2000) (0)
Effect of Sodium Sulphide on the Prevention of Copper Activation for Sphalerite (1968) (0)
Intersection numbers and the Verlinde formula (2003) (0)
Removal of Heavy Metal Ions in Waste Water from Mining Industries by both Coprecipitation and Flotation Methods (1972) (0)
Separation and Concentration of Uranium by Ion Flotation Method (1975) (0)
Separating Conditions for Electro-Static Separation (1958) (0)
The Effect of Dissolved Oxygen on the Reaction between Xanthate and Sulphide Mineral Surface (1970) (0)
Lecture notes on K3 and Enriques surfacesNotes by Sławomir Rams (2012) (0)
On Some Experimental Methods Relating to Flotation (1957) (0)
Flotation Research by the measurement of Electrode Potential (1961) (0)
Rings and polynomials (2000) (0)
Algebraic groups and rings of invariants (2000) (0)
Recent Developments in Non-Sulphide Mineral Dressing (1972) (0)
§ 1 Cremona involution of a quadric surface (2006) (0)
Curves and Grassmannians Dedicated to Prof. Hideyuki Matsumura on his 60th Birthday (2001) (0)
Relation between the Electrode Potential of Sulphide Minerals and their Floatability (1964) (0)
Dedicated to Prof. Robert Lazarsfeld on his 60th birthday (2015) (0)
Recent Development of Iron Ore Concentration (1978) (0)
Effect of Sulfurous Acid on the Floatability of Sulfide Minerals (1968) (0)
Title Numerically trivial involutions of Kummer type of an Enriques (2018) (0)
The projective quotient (2000) (0)
Stable vector bundles on curves (2000) (0)
The numerical criterion and some applications (2000) (0)
Invariants and moduli (2000) (0)
Some Problems on the Flotation of the Complex Sulphide Ores (1966) (0)
Effect of Humidity on the Electrostatic Separation of Coal (1966) (0)
Air-swept raw material grinding mill installation in Abu-Dhabi (1984) (0)
Optoelectronic analog antecedent and consequent fuzzy inference units using LED arrays and position sensing devices (1994) (0)
Algebraic Geometry – in honor of the retirement of Professor Shigeru Mukai – (2019) (0)
Removal of Cadmium and Zinc from the Waste Water by Flotation Method (1972) (0)
Interconnection Architecture Based on Beam-Steering Devices (Special Issue on Optical Interconnection) (1994) (0)
Hodge Theory and Algebraic Geometry (2018) (0)
Study on the Removal of Organic Mercury in Waste Water (1973) (0)
On the Change of the Electronic Surface State of Mineral by the Adsorption of the Dissolved Oxygen (1971) (0)
Thermodynamical Study on the Reaction between Mercury and Xanthate (1963) (0)
Theoretical Considerations for Correlative Effects of Collector Ion and Hydrogen Ion or Hydroxyl Ion on Floatability of Mineral Particles (1962) (0)
BASIC STUDIES ON THE TREATMENT OF FUEL-REPROCESSING LIQUID WASTES BY THE FLOTATION METHOD. VII. SELECTIVE REMOVAL OF MIXED FISSION PRODUCTS. (1968) (0)
Implementation of Optical Ternary Logic Operations Using a Twin-Stripe Laser Diode (1990) (0)
Arithmetic logic unit based on beam-scanning logic architecture (1993) (0)
Fundamental Studies on the Action of Frothing Agents in Sulphide Mineral Flotation (1976) (0)
Optoelectronic fuzzy interface architecture using beam-steering vertical-cavity surface-emitting laser diodes (1998) (0)
Effect of carrier leakage in Q-switched two-section AlGaAs multiple-quantum-well semiconductor lasers (1999) (0)
Algebraic Geometry 2000, Azumino – Program and Acknowledgement (2002) (0)
Consideration for Some Problems and Improved Measures of Separation of Cu-Zn Ores (1977) (0)
Tunable Dual Semiconductor Laser (1987) (0)
Effects of Collector Concentration and Hydrogen Ion Concentration on Flotation of Non-Sulphide Minerals (1961) (0)
Photonic Spatial Logic Operations Using a Beam Scanning Laser Diode (1990) (0)
Parallel-coupled waveguide semiconductor lasers (1984) (0)
Behavior of Mineral Particle in Electro-Static Separation (1958) (0)
Arithmetic and Algebraic Geometry 2015 (2015) (0)
Some Problems concerning the Separation of Copper and Zinc Mineral by Flotation (1967) (0)

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