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Tuomas Tajakka: Uhlenbeck compactification as a Bridgeland moduli space

Time: Tue 2021-11-23 14.30 - 15.30

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, meeting ID: 921 756 1880)

Lecturer: Tuomas Tajakka (Stockholm University)

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.