Numerical invariants of hyper-K\"ahler manifolds
Algebraic Geometry
2025-06-05 v1
Abstract
We study various constraints on the Beauville quadratic form and the Huybrechts-Riemann-Roch polynomial for hyper-K\"ahler manifolds, mostly in dimension 6 and in the presence of an isotropic class. In an appendix, Chen Jiang proves that in general, the Huybrechts-Riemann-Roch polynomial can always be written as a linear combination with nonnegative coefficients of certain explicit polynomials with positive coefficients. This implies that the Huybrechts-Riemann-Roch polynomial satisfies a curious symmetry property
Keywords
Cite
@article{arxiv.2506.04177,
title = {Numerical invariants of hyper-K\"ahler manifolds},
author = {Olivier Debarre and Chen Jiang},
journal= {arXiv preprint arXiv:2506.04177},
year = {2025}
}
Comments
12 pages with an appendix by Chen Jiang