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Character Formulas on Cohomology of Deformations of Hilbert Schemes of K3 Surfaces (1301.6129v2)
Published 25 Jan 2013 in math.AG and math.RT
Abstract: Let X be a hyperkahler manifold deformation equivalent to a Hilbert scheme of n points on a K3 surface. We compute the graded character formula of the generic Mumford-Tate group representation on the cohomology ring of X, and derive a generating series for deducing the number of canonical Hodge classes on X. The formula indicates the number of Hodge classes on X that remain Hodge under any deformation.