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Uhlenbeck compactification as a Bridgeland moduli space

Tuomas Tajakka (UW)
Tuesday, October 13, 2020 - 2:30pm
via Zoom

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.

The talk will start with a pre-seminar at 2pm:

Title: Semistable vector bundles and S-equivalence
Abstract: I will discuss slope-semistable vector bundles on a curve, their moduli theory, and S-equivalence. The main goal is to explain why a moduli variety of semistable vector bundles cannot distinguish S-equivalent bundles.


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