On some birational invariants of hyper-Kähler manifolds

2022/10/22 by Bai, Chenyu
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.12455

Abstract

We study in this article three birational invariants of projective hyper-Kähler manifolds: the degree of irrationality, the fibering gonality and the fibering genus. We first improve the lower bound in a recent result of Voisin saying that the fibering genus of a Mumford--Tate very general projective hyper-Kähler manifold is bounded from below by a constant depending on its dimension and the second Betti number. We also study the relations between these birational invariants for projective K3 surfaces of Picard number 1 and study the asymptotic behaviors of their degree of irrationality and fibering genus.

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