Numerical invariants of hyper-Kähler manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908393647636480 |
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| author | Debarre, Olivier Jiang, Chen |
| author_facet | Debarre, Olivier Jiang, Chen |
| contents | We study various constraints on the Beauville quadratic form and the Huybrechts-Riemann-Roch polynomial for hyper-Kähler 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical invariants of hyper-Kähler manifolds Debarre, Olivier Jiang, Chen Algebraic Geometry 14J42 We study various constraints on the Beauville quadratic form and the Huybrechts-Riemann-Roch polynomial for hyper-Kähler 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 |
| title | Numerical invariants of hyper-Kähler manifolds |
| topic | Algebraic Geometry 14J42 |
| url | https://arxiv.org/abs/2506.04177 |