2005 Fiscal Year Final Research Report Summary
Group theoretic and arithmetic aspects on K3 surfaces
| Project/Area Number |
16540010
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | The University of Tokyo |
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Principal Investigator |
OGUISO Keiji The University of Tokyo, Math.Sci., Associate Professor, 大学院・数理科学研究科, 助教授 (40224133)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAMATA Yujiro The University of Tokyo, Math.Sci., Professor, 大学院・数理科学研究科, 教授 (90126037)
TERASAWA Tomohide The University of Tokyo, Math.Sci., Associate Professor, 大学院・数理科学研究科, 助教授 (50192654)
HOSONO Shinobu The University of Tokyo, Math.Sci., Associate Professor, 大学院・数理科学研究科, 助教授 (60212198)
MATSUO Atsushi The University of Tokyo, Math.Sci., Associate Professor, 大学院・数理科学研究科, 助教授 (20238968)
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| Project Period (FY) |
2004 – 2005
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| Keywords | hyperkahler manifold / K3 surfaces / birational automorphism / Salem polynomial / Mordell-Weil group / entropy / tree group / almost abelian group |
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| Research Abstract |
I have studied group theoretical aspects of the bimeromorphic (birational) automorphism group of a hyperkahler manifold with a help of arithmetical notion "Salem polynomial" and entropy. As a result, among other things, I have obtained the following results :
Theorem 1. Let M be a non-projective hyperkahler manifold.
Then, BicM is an almost abelian group of rank at most max(1,P(M)-1).
Theorem 2. Let M be a projective hyperkahler manifold and G be a subgroup of BicM.
Then, G satisfies either one of :
(i) G is an almost abelian group of rank at most max(1,P(M)-2) ;
(ii) G>Z*Z.
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