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arXiv · 2112.11306

Hodge classes of type (2, 2) on Hilbert squares of projective K3 surfaces

Simone Novario
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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.

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Simone Novario. 2021-12-21. Hodge classes of type (2, 2) on Hilbert squares of projective K3 surfaces. https://arxiv.org/abs/2112.11306

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