SAG: Mumford relations and the cohomology of Le Potier moduli spaces

by Dr Weite Pi

Thursday Oct 16, 2025, 10:30 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

The geometry and topology of Le Potier moduli space, i.e. the moduli of 1-dimensional sheaves on the projective plane, have been studied intensively for decades. One particular interest in this moduli space arises from enumerative geometry — the perverse filtration on cohomology associated with a natural support map encodes the so-called refined BPS invariants for local P^{^2}. Thus it is important to study this cohomology. In this talk, we construct geometrically a family of tautological relations for this moduli space, originally due to Mumford on the moduli of bundles on curves, and derive several structural results on the cohomology. Based on joint works with Yakov Kononov, Woonam Lim, Miguel Moreira, and Junliang Shen.