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Seminars

Algebraic Geometry Seminar

Surface counting on toric Calabi-Yau 4-folds

2024/05/15 (Wed.) 15:30~17:30
  • Date : 2024/05/15 (Wed.) 15:30~17:30
  • Location : online
  • Speaker : Martijn Kool (University of Utrecht)
  • Organizer : Arkadij Bojko's Email: abojko (at) gate (dot) sinica (dot) edu (dot) tw
  • Website : https://wiki.preschema.com/ag-seminar
  • Abstract : On Calabi-Yau 4-folds, there are 3 surface counting theories related by change of polynomial Bridgeland stability condition: DT, PT_0, PT_1. For toric Calabi-Yau 4-folds, I discuss the fixed loci of the moduli spaces for these theories with respect to the 3-dimensional torus preserving the Calabi-Yau volume form. When these fixed loci are 0-dimensional and reduced, I present a method to calculate these invariants by virtual localization using vertex, edge, and face terms (and modulo taking square roots). The DT case also appeared in the physics literature in work of Nekrasov-Piazzalunga. This is joint work with Y. Bae and H. Park.
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