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.
Second Chern class and Fujiki constants of hyperk\"ahler manifolds
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study characteristic classes on hyperk\"ahler manifolds with a view towards the Verbitsky component. The case of the second Chern class leads to a conditional upper bound on the second Betti number in terms of the Riemann--Roch polynomial, which is also valid for singular examples. We discuss the general structure of characteristic classes and the Riemann--Roch polynomial on hyperk\"ahler manifolds using among other things Rozansky--Witten theory.
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math.AG 3representative 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.
The paper enumerates 33 deformation classes of compact hyperkähler orbifolds obtained as terminalizations of quotients of K3 surface products.
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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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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.