Moduli of one-dimensional sheaves: stabilization phenomena and pathologies

主讲人学术背景：张菲诺现为复旦大学上海数学中心博士生（导师：李俊院士）。张菲诺博士研究领域为代数几何，研究方向是层的模空间的计数几何相关问题。
讲座题目：Moduli of one-dimensional sheaves: stabilization phenomena and pathologies
讲座摘要：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.