Moduli of polarized Enriques surfaces

computational aspects

authored by

Mathieu Dutour Sikirić, Klaus Hulek

Abstract

Moduli spaces of (polarized) Enriques surfaces can be described as open subsets of modular varieties of orthogonal type. It was shown by Gritsenko and Hulek that there are, up to isomorphism, only finitely many different moduli spaces of polarized Enriques surfaces. Here we investigate the possible arithmetic groups and show that there are exactly $87$ such groups up to conjugacy. We also show that all moduli spaces are dominated by a moduli space of polarized Enriques surfaces of degree $1240$. Ciliberto, Dedieu, Galati, and Knutsen have also investigated moduli spaces of polarized Enriques surfaces in detail. We discuss how our enumeration relates to theirs. We further compute the Tits building of the groups in question. Our computation is based on groups and indefinite quadratic forms and the algorithms used are explained.

Organisation(s)

Institut für Algebraische Geometrie
Riemann Center for Geometry and Physics

Type

Preprint

Publication date

03.02.2023

Publication status

Elektronisch veröffentlicht (E-Pub)