國立清華大學 數學系

Abstract:
By the Beauville-Bogomolov decomposition theorem, hyper-Kähler manifolds are among the building blocks of Kähler manifolds with trivial first Chern class. After introducing the necessary background, we will discuss the behavior of birational automorphism groups of projective hyper-Kähler manifolds. We will see that these groups are "semicontinuous" in families and that, for nontrivial families of hyper-Kähler manifolds of the known deformation types, the locus of manifolds with infinite birational automorphism groups is dense. This is joint work with Francesco Denisi, Claudio Onorati, and Francesca Rizzo.