Details
| Original language | English |
|---|---|
| Article number | e12828 |
| Number of pages | 32 |
| Journal | Journal of the London Mathematical Society |
| Volume | 109 |
| Issue number | 1 |
| Publication status | Published - 20 Dec 2023 |
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.
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In: Journal of the London Mathematical Society, Vol. 109, No. 1, e12828, 20.12.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Moduli of polarised Enriques surfaces
T2 - Computational aspects
AU - Sikirić, Mathieu Dutour
AU - Hulek, Klaus
N1 - Funding Information: The first author is grateful to DFG for partial support under DFG Hu 337/7‐2 and to Leibniz University Hannover for hospitality. He also thanks G. Nebe and S. Brandhorst for an exchange of ideas at an early stage of then project. We would like to thank A. L. Knutsen for interesting discussions concerning [ 5 ] and him and S. Brandhorst for very helpful comments on a first version of this manuscript.
PY - 2023/12/20
Y1 - 2023/12/20
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85174590239&partnerID=8YFLogxK
U2 - 10.1112/jlms.12828
DO - 10.1112/jlms.12828
M3 - Article
AN - SCOPUS:85174590239
VL - 109
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
SN - 0024-6107
IS - 1
M1 - e12828
ER -