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A note on symplectic singularities
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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.
Forward citations
Cited by 6 Pith papers
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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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A new addition to the zoo of isolated symplectic singularities
A new 4-dimensional isolated locally simply-connected symplectic singularity is constructed, with non-reduced projective tangent cone, together with all 12 of its Q-factorial terminalisations.
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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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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.
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Symplectic resolutions of moduli spaces of $G$-Higgs bundles
M^vc_Dol(G) has symplectic singularities for g≥2 and ss-rank(G)≥2 not pure A1, and its identity component admits no symplectic resolution when G is semisimple with no A1 factor or g≥3.
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