Lehn's formula in Chow and Conjectures of Beauville and Voisin

2019/04/10 by Maulik, Davesh, Neguţ, Andrei
#14C05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1904.05262

Abstract

The Beauville-Voisin conjecture for a hyperkähler manifold X states that the subring of the Chow ring A^*(X) generated by divisor classes and Chern characters of the tangent bundle injects into the cohomology ring of X. We prove a weak version of this conjecture when X is the Hilbert scheme of points on a K3 surface, for the subring generated by divisor classes and tautological classes. This in particular implies the weak splitting conjecture of Beauville for these geometries. In the process, we extend Lehn's formula and the Li-Qin-Wang W_1+infinity algebra action from cohomology to Chow groups, for the Hilbert scheme of an arbitrary smooth projective surface S

Related

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• On product identities and the Chow rings of holomorphic symplectic varieties
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• Finite-dimensionality and cycles on powers of K3 surfaces