2025/06/04 by Olivier Debarre, Chen Jiang, Debarre, Olivier +1
Mathematics · #Geometry and complex manifolds #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2506.04177
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