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

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.

Full Text (PDF format)

Received 4 August 2015

Accepted 23 September 2016

Published 6 March 2018