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Second Chern class and Fujiki constants of hyperk\"ahler manifolds
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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.
Forward citations
Cited by 2 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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Numerical invariants of hyper-K\"ahler manifolds
In dimension six, an isotropic class with extremal intersection numbers forces the Beauville form to be even and the Riemann-Roch polynomial to be one of a short list of explicit polynomials.
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