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# 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: http://dx.doi.org/10.4310/AJM.2017.v21.n6.a4

#### Author

#### 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