Updated on 2024/02/02

写真a

 
KUWATA Masato
 
Organization
Faculty of Economics Professor
Other responsible organization
Electrical Engineering and Information Systems Course of Graduate School of Science and Engineering, Doctoral Program
Contact information
The inquiry by e-mail is 《here
External link

Degree

  • Diplome d’habilitation a diriger des recherches ( Universite de Caen )

  • Ph.D. ( Brown University )

  • M.Sc. ( The University of Tokyo )

Education

  • 1989.5
     

    Brown University   Mathematics   doctor course   completed

  • 1985.3
     

    The University of Tokyo   Graduate School, Division of Science   master course   completed

  • 1983.3
     

    The University of Tokyo   Faculty of Science   graduated

  • 1978.3
     

    東京都立戸山高校   graduated

Research History

  • 2006.4 - Now

    Chuo University   Faculty of Economics   Professor

  • 2021.5 - 2022.3

    Boston Univeristy   Department of Mathematics and Statistics   Visiting Scholar

  • 2004.4 - 2006.3

    Chuo University   Faculty of Economics

  • 2001.4 - 2004.3

    Kanagawa Institute of Technology   Faculty of Engineering

  • 1993.9 - 2001.3

    Université de Caen   UFR de Sciences   Maître de conférences

  • 2000.1 - 2000.9

    The University of Tokyo   Graduate School of Mathematical Sciences

  • 1998.1 - 1998.6

    Brown University   Department of Mathematics   Visiting Assistant Professor

  • 1993.1 - 1993.6

    Concordia University   CICMA   Postdoctoral Fellow

  • 1991.1 - 1992.12

    McGill University   Department of Mathematics and Statistics   NSERC International Postdoctoral Fellow

  • 1990.7 - 1990.11

    University of British Columbia   Postdoctoral Fellow

  • 1989.9 - 1990.5

    Clark University   Department of Mathematics   Visiting Assistant Professor

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Professional Memberships

  • アメリカ数学会

  • 日本数学会

Research Interests

  • Arithmetic Algebraic Geometry

Research Areas

  • Natural Science / Algebra  / Number Theory

  • Natural Science / Algebra  / Algebraic Geomety

Papers

  • Ranks of elliptic curves in cyclic sextic extensions of Q

    Hershy Kisilevsky, Masato Kuwata

    arXiv.org   2023.4

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    Language:English  

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  • Elliptic normal curves of even degree and theta functions

    Masanobu Kaneko, Masato Kuwata

    arXiv.org   2020.5

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  • Mordell–Weil lattice of Inose's elliptic K3 surface arising from the product of 3-isogenous elliptic curves Reviewed

    Masato Kuwata, Kazuki Utsumi

    Journal of Number Theory   190   333 - 351   2018.9

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Academic Press Inc.  

    From the product of two elliptic curves, Shioda and Inose [6] constructed an elliptic K3 surface having two II⁎ fibers. Its Mordell–Weil lattice structure depends on the morphisms between the two elliptic curves. In this paper, we give a method of writing down generators of the Mordell–Weil lattice of such elliptic surfaces when two elliptic curves are 3-isogenous. In particular, we obtain a basis of the Mordell–Weil lattice for the singular K3 surfaces X[3,3,3], X[3,2,3] and X[3,0,3].

    DOI: 10.1016/j.jnt.2018.03.001

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  • Inose's construction and elliptic K3 surfaces with Mordell-Weil rank 15 revisited Reviewed

    Abhinav Kumar, Masato Kuwata

    Contemporary Mathematics   703   131 - 141   2018.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:American Mathematical Society  

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  • Elliptic K3 surfaces associated with the product of two elliptic curves: Mordell-weil lattices and their fields of definition Reviewed

    Abhinav Kumar, Masato Kuwata

    Nagoya Mathematical Journal   228   124 - 185   2017.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Cambridge University Press  

    To a pair of elliptic curves, one can naturally attach two K3 surfaces: The Kummer surface of their product and a double cover of it, called the Inose surface. They have prominently featured in many interesting constructions in algebraic geometry and number theory. There are several more associated elliptic K3 surfaces, obtained through base change of the Inose surface
    these have been previously studied by Masato Kuwata. We give an explicit description of the geometric Mordell-Weil groups of each of these elliptic surfaces in the generic case (when the elliptic curves are non-isogenous). In the nongeneric case, we describe a method to calculate explicitly a finite index subgroup of the Mordell-Weil group, which may be saturated to give the full group. Our methods rely on several interesting group actions, the use of rational elliptic surfaces, as well as connections to the geometry of low degree curves on cubic and quartic surfaces. We apply our techniques to compute the full Mordell-Weil group in several examples of arithmetic interest, arising from isogenous elliptic curves with complex multiplication, for which these K3 surfaces are singular.

    DOI: 10.1017/nmj.2016.56

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  • Equal sums of sixth powers and a certain K3 surface

    Masato Kuwata

    経済学論纂   53 ( 5/6 )   395 - 404   2013.3

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    Language:English   Publisher:中央大学  

    CiNii Books

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  • Vanishing and non-vanishing Dirichlet twists of L-functions of elliptic curves Reviewed

    Jack Fearnley, Hershy Kisilevsky, Masato Kuwata

    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES   86 ( 2 )   539 - 557   2012.10

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:OXFORD UNIV PRESS  

    Let L(E/Q, s) be the L-function of an elliptic curve E defined over the rational field Q. We examine the vanishing and non-vanishing of the central values L(E, 1, chi) of the twisted L-function as chi ranges over Dirichlet characters of a given order.

    DOI: 10.1112/jlms/jds018

    Web of Science

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  • Elliptic parameters and defining equations for elliptic fibrations on a Kummer surface Reviewed

    Masato Kuwata, Tetsuji Shioda

    Algebraic geometry in East Asia - Hanoi 2005   50   177 - 215   2008

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Mathematical Society of Japan  

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  • Equal sums of sixth powers and quadratic line complexes Reviewed

    Masato Kuwata

    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS   37 ( 2 )   497 - 517   2007

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ROCKY MT MATH CONSORTIUM  

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  • Quadratic twists of an elliptic curve and maps from a hyper elliptic curve Reviewed

    Math.Jour. Okayama University   47   85 - 98   2005.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:岡山大学  

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  • Twenty-eight double tangent lines of a plane quartile curve with an involution and the Mordell-Weil lattices Reviewed

    Kuwata Masato

    Comment.Math.Univ. St. Paul   54 ( 1 )   17 - 32   2005.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Rikkyo University  

    CiNii Books

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  • Points defined over cyclic quartic extensions on an elliptic curve and generalized kummer surfaces Reviewed

    M Kuwata

    GALOIS THEORY AND MODULAR FORMS   11   65 - 76   2004

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:SPRINGER  

    Web of Science

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  • 楕円曲線への自明でない写像をもつ代数曲線について

    代数幾何・城崎シンポジウム報告集   2001   51 - 58   2001.4

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    Language:Japanese   Publisher:日本数学会代数分科会  

    CiNii Books

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  • A singular K3 surfaces related to sums of concecutive cubes Reviewed

    Joap Top

    Indagationes Math.   11   419 - 435   2000.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:North-Holland  

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  • Elliptic K3 surfaces with given Mordell-Weil rank Reviewed

    KUWATA M.

    Comment. Math. Univ. St. Paul   49   91 - 110   2000.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:立教大学  

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  • K3曲面とそのMordell-Weil格子

    第45回代数学シンポジウム報告集   2000.4

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    Language:Japanese   Publisher:日本数学会代数学分科会  

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  • Elliptic fibrations on quartic K3 surfaces with large Picard number Reviewed

    Pacific Journal of Math.   171   231 - 243   1995.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Pacific Journal of Math.  

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  • Generalized Artin's conjecture for primitive roots and cyclicity mod p of ellipic curves over function fields Reviewed

    David A. Clark

    Canadian Math. Bull.   38   167 - 173   1995.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Canadian Math. Soc.  

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  • An elliptic surface related to sums of consecutive squares Reviewed

    Joap Top

    Expositiones Math.   12   181 - 192   1994.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Bibliographischos Inst.  

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  • Tordues quadratic de coubes elliptiques et points rationnels sur les surface de Chatlet

    Compte rendus de Journee Arithmetiques   1994.4

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    Language:French   Publisher:universite de Caen  

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  • TOPOLOGY OF RATIONAL-POINTS ON ISOTRIVIAL ELLIPTIC-SURFACES Reviewed

    M KUWATA, L WANG

    DUKE MATHEMATICAL JOURNAL   70 ( 1 )   A113 - A123   1993.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:DUKE UNIV PRESS  

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  • Ramified primes in the field of definition for the Mordell-Weil group of an elliptic surface Reviewed

    Proceedings of Amer. Math. Soc.   116   955 - 959   1992.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:American Mathematical Society  

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  • The canonical height and elliptic surfaces Reviewed

    Journal of Number Theory   36   201 - 211   1990.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Academic Press  

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  • The field of definition of the Mordell-Weil group of an elliptic curve over a function field Reviewed

    Compositio Mathematicae   76   399 - 406   1990.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Kluwer Acad.  

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  • Intersection homology of weighted projective spaces and pseudo-lens spaces Reviewed

    Pacific Journal of Math.   133   355 - 362   1988.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Pacific Journal of Math.  

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Presentations

  • Toward the theory of Mordell-Weil lattices of elliptic threefolds Invited

    Masato Kuwata

    Workshop on Calabi-Yau Varieties and Related Topics 2023  2023.7 

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    Event date: 2023.7    

    Language:English   Presentation type:Oral presentation (invited, special)  

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  • Finding points defined over cyclic sextic extensions of an elliptic curve using a K3 surface Invited

    Masato Kuwta

    Curves over finite fields and arithmetic of K3 surfaces  2022.8 

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    Event date: 2022.8 - 2022.9

    Language:English   Presentation type:Oral presentation (invited, special)  

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  • Finding points defined over cyclic extensions of an elliptic curve: A geometric approach Invited

    Masato Kuwata

    Brown Algebra Seminar  ( Brown University )   2022.2 

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    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • Jacobians of genus 2 curves with full level 3 structure and the related elliptic fibrations Invited

    Masato Kuwata

    Boston University number theory seminar  ( Boston University )   2021.10 

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    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

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  • Rational points on generalized Kummer varieties Invited

    Rational Points on Higher Dimensional Varieties  ( 京都大学数理科学研究所 )   2019.12 

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    Language:English   Presentation type:Oral presentation (invited, special)  

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  • レベル3構造をもつアーベル曲面の普遍族と有理楕円曲面のMordell-Weil格子 Invited

    2018大分鹿児島数論研究集会  ( 鹿児島大学 )   2018.10 

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    Language:Japanese   Presentation type:Oral presentation (invited, special)  

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  • The universal abelian surface with level 3 structure and the Mordell-Weil latice of type E_8

    A Celebration of CICMA's Postdoctoral Program  2018.7 

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  • Shioda-Inose structure and elliptic K3 surfaces with high Mordell-Weil rank

    Geometry and Physics of F-theory, Banff International Research Station 5 Day Workshop  2018.1 

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    Language:English  

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  • Elliptic normal curves of degree 2N and modular groups

    Tsuda College-OIST joint-workshop  2016.8 

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    Language:English  

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  • Elliptic K3 surfaces with Mordell-Weil rank 18

    Arithmetic 2015: Silvermania, Brown University  2015.8 

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  • Elliptic K3 surfaces with high Mordell-Weil rank.

    Workshop on K3 surfaces and Enriques surfaces 2015  2015.8 

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  • Elliptic K3 surfaces with Mordell-Weil rank 18

    Arithmetic and Algebraic Geometry 2015 at University of Tokyo  2015.1 

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Research Projects

  • Mordell-Weil Groups of elliptically-fibered Calabi-Yau manifolds

    Grant number:19K03427  2019.4 - 2024.3

    JSPS  学術研究助成基金助成金  基盤研究(C)  Chuo University

    Masato Kuwata

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    Grant type:Competitive

    Grant amount: \3900000 ( Direct Cost: \3000000 、 Indirect Cost: \900000 )

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  • K3楕円曲面のモーデル・ヴェイユ格子の数論的研究

    2014.4 - 2018.3

    文部科学省  科学研究費助成事業 基盤研究(C) 

    鍬田 政人

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    Grant type:Competitive

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  • 高次元代数多様体の有理点に関する研究

    2014.4 - 2016.3

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    Grant type:Competitive

    Grant amount: \1200000

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  • K3楕円曲面のモーデル・ヴェイユ格子の研究

    2013.4 - 2014.3

    文部科学省  科学研究費助成事業 基盤研究(C) 

    鍬田 政人

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    Grant type:Competitive

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  • Elliptic fibrations on Kummer surfaces

    Grant number:20540022  2008 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  Chuo University

    KUWATA Masato

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    Grant amount: \2080000 ( Direct Cost: \1600000 、 Indirect Cost: \480000 )

    On a K3 surface there may exist more than one elliptic fibration. In order to study detailed arithmetic properties, it is very useful to have many elliptic fibra-tions on a given K3 surface. Our objective is to classify all elliptic fibrations on a given K3 surface and describe them as explicitly as possible. We made a significant progress on this problem in the case of Kummer surfaces associated with curves of genus 2. We also ob-tained some interesting results on K3 surfaces related to modular elliptic surfaces.

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  • 高次元代数多様体の有理点について

    2007.4 - 2008.9

    中央大学  中央大学特定課題研究費 

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    Grant type:Competitive

    Grant amount: \900000

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  • 代数曲面および高次元代数多様体の有理点について

    2005.4 - 2006.9

    中央大学  中央大学特定課題研究費 

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    Grant type:Competitive

    Grant amount: \900000

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  • Special Linear System on an Algebraic Curve and its Application

    Grant number:15540035  2003 - 2004

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  The University of Tokushima

    OHBUCHI Akira, KATO Takao, KOMEDA Jiryo, HOMMA Masaaki, KUWATA Masato

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    Grant amount: \2700000 ( Direct Cost: \2700000 )

    Let W^r_d(C) be a scheme of line bundles defined by W^r_d(C)={L|L∈Pic^d(C),dimΓ(C,L)【greater than or equal】r+1} (usually, W^r_d(C) can be defined as a subscheme of Pic^d(C)). Kempf and Kleiman-Laksov prove that the variety W^r_d(C) has dimension at least p=g-(r+l)(g-d+r). Griffith-Harris and Fulton-Lazarsfeld prove that W^r_d(C) is smooth of dimension p=g-(r+1)(g-d+r) when C is a general curve in the moduli spaceM_g. "A general curve" means there is an open subset U⊂M_g inM_g, W^r_d(C) is smooth of dimension p=g-(r+1)(g-d+r) for any curve C∈U. So it is natural to ask to classify which curve belongs to this open subset U⊂M_g. As for this problem, we can give good sufficient conditions (No.2 and No.3).
    For a finitely generated numerical semigroup which start from 4, Komeda proved that every such numerical semigroup H is Weierstrass, i.e. there is a pointed curve (C,P) such that the semigroup of non-gaps of P is just H. Unfortunatelly, in Komeda's argument, (C,P) is not constructive for some special type numerical semigroups, i.e. he uses some general theory of torus embedding and proved only the existence of (C,P). So it is very natural to ask whether a pointed curve (C,P) can be constructed concretely for this special type numerical semigroups. Our result is that we can construct (C,P) for such special type semigroup by using a double covering of hyperelliptic curve which is n-sheeted covering of another hyperelliptic curve.(No.1)

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