Asian Journal of Mathematics

Volume 21 (2017)

Number 6

Universal covering Calabi–Yau manifolds of the Hilbert schemes of $n$ points of Enriques surfaces

Pages: 1099 – 1120

DOI: https://dx.doi.org/10.4310/AJM.2017.v21.n6.a4

Author

Taro Hayashi (Department of Mathematics, Graduate School of Science, Osaka University, Osaka, Japan)

Abstract

The purpose of this paper is to investigate the Hilbert scheme of $n$ points of an Enriques surface from the following three points of view: (i) the relationship between the small deformation of the Hilbert scheme of $n$ points of an Enriques surface and that of its universal cover (Theorem 1.1), (ii) the natural automorphisms of the Hilbert scheme of $n$ points of an Enriques surface (Theorem 1.4), and (iii) the number of distinct Hilbert schemes of $n$ points of Enriques surfaces, which has the same universal covering space (Theorem 1.7).

Keywords

Calabi–Yau manifold, Enriques surface, Hilbert scheme

2010 Mathematics Subject Classification

Primary 14J32. Secondary 14J28.

Received 4 August 2015

Accepted 23 September 2016

Published 6 March 2018