On the irrationality of moduli spaces of projective hyperkähler manifolds
Daniele Agostini, Ignacio Barros, Kuan-Wen Lai
Published: 2023/7/14
Abstract
The aim of this paper is to estimate the irrationality of moduli spaces of hyperk\"ahler manifolds of types K3$^{[n]}$, Kum$_{n}$, OG6, and OG10. We prove that the degrees of irrationality of these moduli spaces are bounded from above by a universal polynomial in the dimension and degree of the manifolds they parametrize. We also give a polynomial bound for the degrees of irrationality of moduli spaces of $(1,d)$-polarized abelian surfaces.