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Seminars

Algebraic Geometry Seminar

Spin structures on quadratic complexes

2024/05/10 (Fri.) 10:00~12:00
  • Date : 2024/05/10 (Fri.) 10:00~12:00
  • Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
  • Speaker : Nick Kuhn (University of Oslo)
  • Organizer : Arkadij Bojko's Email: abojko (at) gate (dot) sinica (dot) edu (dot) tw
  • Website : https://wiki.preschema.com/ag-seminar
  • Abstract : We present a notion of spin structure for a perfect complex E (on a complex variety X) which is equipped with an oriented quadratic structure. The existence of a spin structure on E is obstructed by a natural Z/2Z-gerbe over X, carrying a universal spin structure. As an application we show how to construct a twisted virtual structure sheaf on moduli spaces of sheaves on Calabi-Yau fourfolds. A-priori, it exists as a Z/2Z-graded sheaf on the spin-gerbe over the moduli space M. We expect that it induces a natural class in the K-theory of M with 2 inverted, which agrees with the Oh-Thomas class.
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