Department of Mathematics,
University of California San Diego
****************************
Math 208: Seminar in Algebraic Geometry
Dr. Yinbang Lin
University of Houston
Expected behaviors of sheaves on algebraic surfaces
Abstract:
Motivated by the Brill--Noether problems and enumerative geometry over surfaces, we study the expected behaviors of coherent sheaves. We estimate the dimension of global sections of stable sheaves. We also prove some cases of an analogue of Lange's conjecture over curves, which states that general extensions of two vector bundles are stable under some obvious conditions. These are closely related to Segre invariants of sheaves, which studies maximal subsheaves of a fixed rank. This can be understood as to determine when Grothendieck's Quot schemes are non-empty. This is based on work in progress jointly with Thomas Goller and Zhixian Zhu.
Host: Dragos Oprea
January 16, 2026
4:00 PM
APM 7321
Research Areas
Algebraic Geometry****************************
