Algebraic Geometry Seminar
Dawei Chen
Boston College
Counting differentials with fixed residues
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.
Monday March 4, 2024 at 3:00 PM in 636 SEO