Numerical invariants of hyper-K\"ahler manifolds

Olivier Debarre; Chen Jiang

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arXiv · 2506.04177

Numerical invariants of hyper-K\"ahler manifolds

Olivier Debarre·Chen Jiang

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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

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BibTeX RIS

Olivier Debarre, Chen Jiang. 2025-06-04. Numerical invariants of hyper-K\"ahler manifolds. https://arxiv.org/abs/2506.04177

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