Description:

Title: Hodge modules on toric varieties

Abstract: The intersection cohomology complex IC_X on a toric variety X has been well studied starting with the works of Stanley and Fieseler, and more recently, the works of de Cataldo-Migliorini-Mustata and Saito. However, it has a richer structure as a Hodge module (denoted IC^H_X) in the sense of Saito’s theory, and so we have the graded de Rham complexes gr_k(DR(IC^H_X)), which are complexes of coherent sheaves carrying significant information about X. In this talk, I will describe the generating function of the cohomology sheaves of gr_k(DR(IC^H_X)) and give a precise formula relating it with the stalks of the perverse sheaf IC_X (in particular, this implies that the generating function depends only on the combinatorial data of the toric variety). Time permitting, I will also show that the generating function can be computed explicitly in an algorithmic way. This is joint work with Hyunsuk Kim.