Hodge integrals

We reformulate a conjecture of Deligne on 1-motives by using the integral weight filtration of Gillet and Soul´ on cohomology, and prove it. This implies e the original conjecture up to isogeny. If the degree of cohomology is at most two, we can prove the conjecture for the Hodge realization without isogeny, and even for 1-motives with torsion. j Let X be a complex algebraic variety. We denote by H(1) (X, Z) the maximal mixed Hodge structure of type {(0, 0), (0, 1), (1, 0), (1, 1)} contained in j j H j (X, Z). Let H(1) (X, Z)fr...

42p tuanloccuoi 04-01-2013 46 7   Download

We prove a closed formula for integrals of the cotangent line classes against the top Chern class of the Hodge bundle on the moduli space of stable pointed curves. These integrals are computed via relations obtained from virtual localization in Gromov-Witten theory. An analysis of several natural matrices indexed by partitions is required. 0. Introduction 0.1. Overview. Let Mg,n denote the moduli space of nonsingular genus g curves with n distinct marked points (over C).

29p tuanloccuoi 04-01-2013 54 7   Download