Seminar:Moduli of one-dimensional sheaves: stabilization phenomena and pathologies

Seminar| Institute of Mathematical Sciences

Time:Wednesday, May 21th, 2025,15:00-16:00

Abstract:Moduli spaces of sheaves on surfaces have played an important role in many areas, yet a lot of natural questions about them remain unanswered. Motivated by stabilization phenomena of moduli of torsion free sheaves, we wonder if the moduli space of one-dimensional sheaves supported on sufficiently positive divisors on a surface behaves as nicely as expected. In this talk, I will report recent progress on the stabilization of Betti and Picard numbers of moduli of one-dimensional sheaves on surfaces, along with unexpected examples of reducible moduli spaces in the case of certain surfaces of general type. This talk is based on joint works with Weite Pi, Junliang Shen, and Fei Si.