Uhlenbeck compactification as a Bridgeland moduli space

Thursday, October 22, 2020 - 2:00pm
Tuomas Tajakka
University of Washington

Abstract: In recent years, Bridgeland stability conditions have become a central tool in the study of moduli of sheaves and their birational geometry. However, moduli spaces of Bridgeland semistable objects are known to be projective only in a limited number of cases. After reviewing the classical moduli theory of sheaves on curves and surfaces, I will present a new projectivity result for a Bridgeland moduli space on an arbitrary smooth projective surface, as well as discuss how to interpret the Uhlenbeck compactification of the moduli of slope stable vector bundles as a Bridgeland moduli space. The proof is based on studying a determinantal line bundle constructed by Bayer and Macrì. Time permitting, I will mention some ongoing work on PT-stability on a 3-fold.

Zoom link: https://umsystem.zoom.us/j/97020955781?pwd=MTRuWEEzajRWd0JxTE96OFlTd2VoQT09