Group theoretic and arithmetic aspects on K3 surfaces

点击翻译按钮获取中文摘要

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.