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Projective orbifolds of Nikulin type

Chiara Camere, Alice Garbagnati, Grzegorz Kapustka and Michał Kapustka

Vol. 18 (2024), No. 1, 165–208
Abstract

We study projective irreducible symplectic orbifolds of dimension four that are deformations of partial resolutions of quotients of hyperkähler manifolds of K3[2]-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 K3[2]-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 (3,4) in 6.

Keywords
Irreducible symplectic manifolds, Irreducible symplectic orbifolds, symplectic automorphisms, 4-folds
Mathematical Subject Classification
Primary: 14J35, 14J42
Secondary: 14J10, 14J50
Supplementary material

M2Code

Milestones
Received: 21 February 2022
Revised: 22 November 2022
Accepted: 13 February 2023
Published: 22 November 2023
Authors
Chiara Camere
Dipartimento di Matematica
Università degli Studi di Milano
Milano
Italy
Alice Garbagnati
Dipartimento di Matematica
Università degli Studi di Milano
Milano
Italy
Grzegorz Kapustka
Department of Mathematics and Informatics
Jagiellonian University
Kraków
Poland
Michał Kapustka
Institute of Mathematics of the Polish Academy of Sciences
Warsaw
Poland

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