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arXiv · 2201.07767

Second Chern class and Fujiki constants of hyperk\"ahler manifolds

Thorsten Beckmann·Jieao Song
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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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Thorsten Beckmann, Jieao Song. 2022-01-19. Second Chern class and Fujiki constants of hyperk\"ahler manifolds. https://arxiv.org/abs/2201.07767

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