A higher-dimensional Kummer construction associates K3^[3]-type hyper-Kähler sixfolds to Kum^3-type sixfolds, with applications to motives, derived categories, and algebraic cycle conjectures.
A note on symplectic singularities
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
abstract
In this paper we shall prove that the singular locus of a symplectic singularity has no codimension 3 irreducible components. As a corollary, a symplectic singularity is terminal if and only if its singular locus has codimension $\geq 4$. It is hoped that a symplectic singularity has much stronger properties.
representative citing papers
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.
Affine closure of T*O_n in sl_n is isomorphic via C*-Hamiltonian reduction to the minimal nilpotent orbit closure in so_{2n+2}, and has no symplectic resolution.
The paper enumerates 33 deformation classes of compact hyperkähler orbifolds obtained as terminalizations of quotients of K3 surface products.
Extends the LLV algebra to primitive symplectic varieties with isolated singularities via an isomorphism g ≅ so((IH²(X,Q), Q_X) ⊕ h) and studies the resulting representation theory with applications to the P=W conjecture.
citing papers explorer
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The hyper-Kummer construction
A higher-dimensional Kummer construction associates K3^[3]-type hyper-Kähler sixfolds to Kum^3-type sixfolds, with applications to motives, derived categories, and algebraic cycle conjectures.
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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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A connection between minimal nilpotent orbits of types A and D via Hamiltonian reduction
Affine closure of T*O_n in sl_n is isomorphic via C*-Hamiltonian reduction to the minimal nilpotent orbit closure in so_{2n+2}, and has no symplectic resolution.
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Thirty-three deformation classes of compact hyperk\"ahler orbifolds
The paper enumerates 33 deformation classes of compact hyperkähler orbifolds obtained as terminalizations of quotients of K3 surface products.
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The LLV Algebra for Primitive Symplectic Varieties with Isolated Singularities
Extends the LLV algebra to primitive symplectic varieties with isolated singularities via an isomorphism g ≅ so((IH²(X,Q), Q_X) ⊕ h) and studies the resulting representation theory with applications to the P=W conjecture.