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2000 Fiscal Year Final Research Report Summary

Research on K3 surfaces

Research Project

Project/Area Number 10440005
Research Category

Grant-in-Aid for Scientific Research (B).

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

KONDO Shigeyuki  Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (50186847)

Co-Investigator(Kenkyū-buntansha) TANIGAWA Yoshio  Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (50109261)
NAMIKAWA Yukihiko  Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (20022676)
MUKAI Shigeru  Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (80115641)
SANO Takeshi  Nagoya University, Graduate School of Mathematics, Assistant Professor, 大学院・多元数理科学研究科, 助手 (90252220)
YOSHIKAWA Ken-ichi  University of Tokyo, Graduate School of Mathematics, Associate Professor, 大学院・数理科学研究科, 助教授 (20242810)
Project Period (FY) 1998 – 2000
KeywordsK3 surface / Enriques surface / Moduli space / Automorphic forms / Curve / Complex ball / Del Pezzo surface / Arithmetic subgroup
Research Abstract

(1) A projective model of the moduli space of Enriques surfaces.
It is known that the moduli space of Enriques surfaces can be described as an arithmetic quotient of a bounded symmetirc domian of type IV.We apply Borcherds theory on automorphic forms on type IV domain to the case of Enriques surface and constructed a birational map from the moduli space of Enriques surfaces with level 2 structure into P^<185>.
(2) A ball quotient structure of the moduli space of curves of genus 4.
We showed that the moduli space of curves of genus 4 is birational to an arithmetic quotient of 9-dimensional complex ball by using the theory of periods of K3 surfaces. Moreover we proved that this arithmetic group is commensurable to one of Deligne-Mostow' complex reflection groups related to hypergeometric equations. And we showed that the moduli space of del Pezzo surfaces is also related to K3 surfaces.

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] S.Kondo: "A complex hyperbolic structure for the moduli space of curves of genus three"Journal fur die reine und angewandte Mathematik. 525. 219-232 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Kondo: "The moduli space of Enriques surfaces and Borcherds products"J.Algebraic Geometry. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Kondo: "The moduli space of curves of genus 4 and Deligne-Mostow's complex reflection groups"Proc.Advanced Studies. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Akiyama,Y.Tanigawa: "A mean value for the approximate functional equation of ζ_2(s) for short intervals"J.Ramanujan Math.Soc.. 15. 53-70 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Tanigawa 他: "Analytic continuation of multiple zeta functions and their values at non-positive integers"Acta Arith.. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 吉川謙一: "Analytic torsions and automorphic forms on moduli spaces"数学. 52. 142-158 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 向井茂: "モジュライ理論II(現代数学の展開、青本和彦等編)"岩波書店. 455 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Kondo: "A complex hyperbolic structure for the moduli space of curves of genus three."Journal fur die reine und angewandte Mathematik. 525. 219-232 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Kondo.: "The moduli space of Enriques surfaces and Borcherds products."Journal of Algebraic Gecmethy. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Kondo.: "The moduli of curves of genus 4 and Deligne-Mostow's complex reflection groups."Advanced Studies in Mathematics. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Akiyama, Y.Tanigawa.: "A mean value for the approximate functional equation of ζ_2 (s) for short intervals."J.Ramanujan Math.Soc.. 15. 53-70 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Tanigawa.: "Analytic continuation of multiple zeta functions and their values at non-positive integers."Acta Arith.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Yoshikawa.: "Analytic torsions and automorphic forms on moduli spaces"Sugaku. 52(in Japanese). 142-158 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Mukai: "Moduli Theory II."Iwanami. 455 (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2002-03-26   Modified: 2021-12-10  

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