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Projective orbifolds of
Nikulin type
Chiara Camere, Alice Garbagnati, Grzegorz Kapustka and Michał Kapustka |
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Vol. 18 (2024), No. 1, 165–208
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Abstract |
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We study projective irreducible symplectic orbifolds of dimension four that are deformations of partial resolutions of quotients of hyperkähler manifolds of -type by symplectic involutions; we call them orbifolds of Nikulin type. We first classify those projective orbifolds that are really quotients, by describing all families of projective fourfolds of -type with a symplectic involution and the relation with their quotients, and then study their deformations. We compute the Riemann–Roch formula for Weil divisors on orbifolds of Nikulin type and using this we describe the first known locally complete family of singular irreducible symplectic varieties as double covers of special complete intersections in . |
Keywords
irreducible symplectic manifolds, irreducible symplectic
orbifolds, symplectic automorphisms, 4-folds
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Mathematical Subject Classification
Primary: 14J35, 14J42
Secondary: 14J10, 14J50
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Supplementary material |
Milestones
Received: 21 February 2022
Revised: 22 November 2022
Accepted: 13 February 2023
Published: 22 November 2023
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Authors |
| Chiara Camere | |
| Dipartimento di Matematica Università degli Studi di Milano Milano Italy |
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| Alice Garbagnati | |
| Dipartimento di Matematica Università degli Studi di Milano Milano Italy |
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| Grzegorz Kapustka | |
| Department of Mathematics and
Informatics Jagiellonian University Kraków Poland |
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| Michał Kapustka | |
| Institute of Mathematics of the
Polish Academy of Sciences Warsaw Poland |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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