English

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'