Moduli of polarised Enriques surfaces — Computational aspects

Dutour Sikirić, Mathieu; Hulek, Klaus (2023) Moduli of polarised Enriques surfaces — Computational aspects. Journal of the London Mathematical Society, 109 (1). ISSN 0024-6107

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Abstract

Moduli spaces of (polarised) 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 polarised 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 polarised Enriques surfaces of degree 1240. Ciliberto, Dedieu, Galati and Knutsen have also investigated moduli spaces of polarised 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.

Item Type:	Article
Uncontrolled Keywords:	moduli spaces; polarised Enriques surfaces; permutation group algorithms
Subjects:	NATURAL SCIENCES > Mathematics
Divisions:	Division for Marine and Enviromental Research
Depositing User:	Ivana Vuglec
Date Deposited:	02 Apr 2026 08:58
URI:	http://fulir.irb.hr/id/eprint/11566
DOI:	10.1112/jlms.12828

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