On some birational invariants of hyper-K\"ahler manifolds
Algebraic Geometry
2022-10-25 v1
Abstract
We study in this article three birational invariants of projective hyper-K\"ahler 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-K\"ahler 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.
Keywords
Cite
@article{arxiv.2210.12455,
title = {On some birational invariants of hyper-K\"ahler manifolds},
author = {Chenyu Bai},
journal= {arXiv preprint arXiv:2210.12455},
year = {2022}
}