Second Chern class and Fujiki constants of hyperkähler manifolds

Beckmann, Thorsten; Song, Jieao

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Second Chern class and Fujiki constants of hyperkähler manifolds

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Beckmann, Thorsten
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2201.07767
(Preprint)

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Citation

Beckmann, T., & Song, J. (submitted). Second Chern class and Fujiki constants of hyperkähler manifolds.

Cite as: https://hdl.handle.net/21.11116/0000-000F-6DAD-5

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.