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Algebraic Geometry Seminar

Mumford relations, Virasoro representations, and moduli of one-dimensional sheaves

  • Date : 2024/05/22 (Wed.) 10:00~12:00
  • Location : online
  • Speaker : Weite Pi (Yale University)
  • Organizer : Arkadij Bojko's Email: abojko (at) gate (dot) sinica (dot) edu (dot) tw
  • Website : https://wiki.preschema.com/ag-seminar
  • Abstract : I will report recent progress on the cohomology of the moduli of one-dimensional sheaves on the projective plane. This moduli space relates intimately to the enumerative geometry of local P^2 via a certain perverse filtration on its cohomology, which is in turn determined by the cohomology ring structure. I will explain a systematic approach to study this cohomology ring. Our main ingredients include Mumford-type geometric relations and a representation of the (half) Virasoro algebra on the cohomology of the moduli spaces. Time permitting, I will also discuss a conjectural description of the perverse filtration in terms of explicit tautological classes. Based on joint work with Y. Kononov, W. Lim, and M. Moreira.