Affiliation:
1. Sorbonne Université and Université de Paris , CNRS, IMJ-PRG, F-75005 Paris, France
Abstract
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.
Publisher
Oxford University Press (OUP)
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