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Riemann-Roch Polynomials of the known Hyperk\"ahler Manifolds

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arxiv 2006.09307 v3 pith:TVANNW5C submitted 2020-06-16 math.AG

Ángel David Ríos Ortiz This is my paper · ORCID
classification math.AG
keywords ahlercomputeformulashyperkmanifoldsappendixbundlescharacteristic
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We compute explicit formulas for the Euler characteristic of line bundles in the two exceptional examples of Hyperk\"ahler Manifolds introduced by O'Grady. In the Appendix Yalong Cao and Chen Jiang use our formulas to compute the Chern numbers for the 10-dimensional example.

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  1. Numerical invariants of hyper-K\"ahler manifolds

    math.AG 2025-06 conditional novelty 6.0 of 10

    In dimension six, an isotropic class with extremal intersection numbers forces the Beauville form to be even and the Riemann-Roch polynomial to be one of a short list of explicit polynomials.

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