Second Chern class and Fujiki constants of hyperk\"ahler manifolds
Algebraic Geometry
2022-08-09 v2
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.
Keywords
Cite
@article{arxiv.2201.07767,
title = {Second Chern class and Fujiki constants of hyperk\"ahler manifolds},
author = {Thorsten Beckmann and Jieao Song},
journal= {arXiv preprint arXiv:2201.07767},
year = {2022}
}
Comments
25 pages; added an appendix on the singularities of the orbifold K4'