The partition function of Calabi-Yau threefolds with torsion

Date: 2022-07-25

Time: 14:30 - 15:30


Sheldon Katz


The complexified Kahler moduli space of a Calabi-Yau X threefold splits into disjoint components indexed by the torsion subgroup of H^3(X,Z), leading to multiple partition functions, all controlled by the Gopakumar-Vafa or Gromov-Witten invariants.  These partition functions can be computed in many cases by B-model techniques, leading to predictions for the GV invariants in low degree.  It is natural to conjecture that each component of Kahler moduli parametrizes Bridgeland stability conditions on a derived category of twisted sheaves, the twisting coming from the corresponding element of the Brauer group of X.  The main example discussed in this talk is a non-Kahler small resolution X of the double cover of P^3 branched along a determinantal octic.  Many of the predicted GV invariants can be confirmed by enumerative geometry after showing that the exceptional P^1’s all represent 2-torsion classes in H_2(X,Z).