On the irrationality of moduli spaces of projective hyperk\"ahler manifolds

Author:

Daniele Agostini, Ignacio Barros, Kuan-Wen Lai

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)

journal:

date:

2023-07-13 16:00:00

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.

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