2000 Fiscal Year Final Research Report Summary
| Project/Area Number |
10440005
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| Research Category |
Grant-in-Aid for Scientific Research (B).
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Nagoya University |
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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)
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| 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)
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| Project Period (FY) |
1998 – 2000
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| Keywords | K3 surface / Enriques surface / Moduli space / Automorphic forms / Curve / Complex ball / Del Pezzo surface / Arithmetic subgroup |
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| 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.
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