Dawei Chen : Counting differentials with fixed residues

Posted by Gwyneth Moreland , part of the Algebraic Geometry Seminar.

At

March 4, 2024, 3 p.m.

In

636 SEO

Abstract

We investigate the count of meromorphic differentials on the Riemann sphere possessing a single zero, multiple poles with prescribed orders, and fixed residues at each pole. Gendron and Tahar previously examined this problem with respect to general residues using flat geometry, while Sugiyama approached it from the perspective of fixed-point multipliers of polynomial maps in the case of simple poles. In our study, we employ intersection theory on compactified moduli spaces of differentials, enabling us to handle arbitrary residue conditions and provide a complete solution to this problem. This is joint work with Miguel Prado.