ファイル更新日：2007年12月07日

アーカイブ

■KIASとの学術交流協定締結記念講演会■

●日　　時

2004年2月26日　15:30〜16:30

●会　　場

理1号館　509講義室　名古屋大学大学院多元数理科学研究科

●プログラム

●タイトル

“Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic”

●アブストラクト

A remarkable work of S. Mukai gives a classification of finite groups which can act on a complex algebraic K3 surface leaving invariant its holomorphic 2-form (symplectic automorphism groups). Any such group turns out to be isomorphic to a subgroup of the Mathieu group M₂₃ which has at least 5 orbits in its natural action on the set of 24 elements. A list of maximal subgroups with this property consists of 11 groups, each of these can be realized on an explicitly given K3 surface. The subsequent proofs of Mukai's result were given by different methods by S. Kondo and Xiao. None of these proofs extends to the case of K3 surfaces over algebraically closed fields of positive characteristic p.

In this talk we outline a joint work with I. Dolgachev, namely that the ideas of Mukai's proof can be extended to positive characteristic p > 11, and consequently that we have the same list of groups for p > 11.

For p ≤ 11 there are known examples of K3 surfaces over a field of characteristic p whose automorphism group contains a finite symplectic subgroup which is not realized as a subgroup of M₂₃.