# Tuomas Tajakka: Uhlenbeck compactification as a Bridgeland moduli space

**Time: **
Wed 2021-11-03 13.15 - 14.15

**Location: **
Zoom, meeting ID: 694 6016 6420 (password required)

**Lecturer: **
Tuomas Tajakka (SU)

**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 work on PT-stability on a 3-fold.

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