Hodge classes of type (2, 2) on Hilbert squares of projective K3 surfaces
Algebraic Geometry
2022-01-11 v2
Abstract
We give a basis for the vector space generated by rational Hodge classes of type (2,2) on the Hilbert square of a projective K3 surface general in its rank, which is a subspace of the singular cohomology ring with rational coefficients: we use Nakajima operators and an algebraic model developed by Lehn and Sorger as main tools. We then obtain a basis of the lattice generated by integral Hodge classes of type (2,2) on the Hilbert square of a projective K3 surface general in its rank: we exploit lattice theory, a theorem by Qin and Wang and a result by Ellingsrud, G\"ottsche and Lehn.
Cite
@article{arxiv.2112.11306,
title = {Hodge classes of type (2, 2) on Hilbert squares of projective K3 surfaces},
author = {Simone Novario},
journal= {arXiv preprint arXiv:2112.11306},
year = {2022}
}
Comments
Statements of Theorem 6.2 and Theorem 8.3 corrected, Remark 6.3 added. 22 pages, comments are welcome