Algebraic Geometry Seminar
Master spaces, obstruction theories, and well-defined invariants
2024/10/25 (Fri.) 15:00~17:00
- Date : 2024/10/25 (Fri.) 15:00~17:00
- Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
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Speaker : Arkadij Bojko (AS)
- Organizer : Ionut Ciocan-Fontanine and Adeel Khan and Y.P. Lee (AS)
- Abstract : I will start by introducing some notation for Calabi-Yau dg-quivers. This language comes in handy once one starts talking about the obstruction theories of enhanced master spaces for the purpose of wall-crossing. For quiver representations, these obstruction theories can be constructed explicitly by geometric arguments. Apart from some very simple cases, the direct construction does not go through for sheaves due to potential obstructions. Thanks to the Jouanolou's trick, one can pretend that these obstructions vanish by working over affines. Lastly, the invariants counting semistable sheaves need to be defined even in the presence of strictly semistables. I will finish with the proof that this definition for torsion-free sheaves is independent of choices. The statement holds in full generality, but only in this setting it can be understood truely geometrically.
