The Chow ring of the moduli space of degree 2 quasi-polarized K3 surfaces

2023/07/18 by Canning, Samir, Oprea, Dragos, Pandharipande, Rahul · 1 citation
#14C15 #14C17 #14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.09284

Abstract

We study the Chow ring with rational coefficients of the moduli space \mathcal F₂ of quasi-polarized K3 surfaces of degree 2. We find generators, relations, and calculate the Chow Betti numbers. The highest nonvanishing Chow group is \mathsf A¹⁷(\mathcal F₂)≅ ℚ. We prove that the Chow ring consists of tautological classes and is isomorphic to the even cohomology. The Chow ring is not generated by divisors and does not satisfy duality with respect to the pairing into \mathsf A¹⁷(\mathcal F₂). The kernel of the pairing is a 1-dimensional subspace of A⁹(\mathcal F₂) which we calculate explicitly. In the appendix, we revisit Kirwan-Lee's calculation of the Poincaré polynomial of F₂.

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• K-theory of Weighted Blowups

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