Universal covering calabi-yau manifolds of the Hilbert schemes of n points of Enriques surfaces

Abstract

Throughout this paper, we work over $\mathbb{C}$, and $n$ is an integer such that $n\ge 2$. For an Enriques surface $E$, let $E^{[n]}$ be the Hilbert scheme of $n$ points of $E$. By Oguiso and Schröer, $E^{[n]}$ has a Calabi-Yau manifold $X$ as the universal covering space, $\pi :X\to E^{[n]}$ of degree $2$. The purpose of this paper is to investigate a relationship of the small deformation of $E^{[n]}$ and that of $X$ $(\mathrm{Theorem}1.1)$, the natural automorphism of $E^{[n]}$ $(\mathrm{Theorem}1.2)$, and count the number of isomorphism classes of the Hilbert schemes of $n$ points of Enriques surfaces which has $X$ as the universal covering space when we fix one $X$ $(\mathrm{Theorem}1.3)$.

17 pages

References in corpus (1)

• A question of Doctor Malte Wandel on automorphisms of the punctural Hilbert schemes of K3 surfaces