Oct

23

2024

When:
Wednesday, October 23, 2024

3:00 PM - 4:00 PM CT

Where: Lunt Hall, 107, 2033 Sheridan Road, Evanston, IL 60208 map it

Audience: Faculty/Staff - Student - Public - Post Docs/Docs - Graduate Students

Contact:
Yuchen Liu

Group: Department of Mathematics: Algebraic Geometry Seminar

Category: Lectures & Meetings

**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.