Multiplicativity of Perverse Filtration for Hilbert Schemes of Fibered Surfaces

2015/12/15 by Zhang, Zili · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.04643

Abstract

Let S→ C be a smooth projective surface with numerically trivial canonical bundle fibered onto a curve. We prove the multiplicativity of the perverse filtration with respect to the cup product on H^*(S^[n],ℚ) for the natural morphism S^[n]→ C⁽ⁿ⁾. We also prove the multiplicativity for five families of Hitchin systems obtained in a similar way and compute the perverse numbers of the Hitchin moduli spaces. We show that for small values of n the perverse numbers match the predictions of the numerical version of the de Cataldo-Hausel-Migliorini P=W conjecture and of the conjecture by Hausel, Letellier and Rodriguez-Villegas.

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• Local multiplicativity of perverse filtrations

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