Classification of terminalizations of symplectic quotients of K3^{[n]} and generalized Kummer varieties yields at least nine new deformation types of irreducible symplectic varieties of dimension four.
Thirty-three deformation classes of compact hyperk\"ahler orbifolds
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
As their smooth analogue the irreducible symplectic varieties appear as elementary bricks in the generalizations of the Bogomolov decomposition theorem (arXiv:math/0402243, arXiv:2012.00441). Let $S$ be a K3 surface; generalizing the Fujiki construction, we investigate the irreducible symplectic varieties with simply connected smooth locus that can be obtained as terminalizations of quotients of the product $S^{n}$. In dimension 4, we compute the singularities for 29 orbifolds examples which appear to be independent under deformation. We also provide 4 additional orbifolds examples in dimension 6.
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UNVERDICTED 3representative citing papers
Constructs irreducible symplectic varieties of dimension 2n (2≤n≤10) with 16≤b2≤24 as non-trivial terminalisations of finite symplectic quotients of Beauville-Mukai systems on very general K3-del Pezzo double covers.
Monodromy group of Nikulin-type orbifolds is maximal; finite order symplectic automorphisms classified up to deformation via action on second integral cohomology.
citing papers explorer
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Terminalizations of quotients of compact hyperk\"ahler manifolds by induced symplectic automorphisms
Classification of terminalizations of symplectic quotients of K3^{[n]} and generalized Kummer varieties yields at least nine new deformation types of irreducible symplectic varieties of dimension four.
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Irreducible symplectic varieties via K3-del Pezzo double covers
Constructs irreducible symplectic varieties of dimension 2n (2≤n≤10) with 16≤b2≤24 as non-trivial terminalisations of finite symplectic quotients of Beauville-Mukai systems on very general K3-del Pezzo double covers.
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Automorphisms of Nikulin-type orbifolds
Monodromy group of Nikulin-type orbifolds is maximal; finite order symplectic automorphisms classified up to deformation via action on second integral cohomology.