Seminar in Real and Complex Geometry

Thursday, May 4, 2023, 17:15-18:45, online via zoom

Sheldon Katz
(University of Illinois at Urbana-Champaign)

Enumerative Invariants of Calabi-Yau Threefolds with Torsion and Noncommutative Resolutions


A Calabi-Yau threefold X with torsion in H_2(X,Z) has a disconnected complexified Kahler moduli space and multiple large volume limits. B-model techniques and mirror symmetry need to be applied at all of these large volume limits in order to extract the Gromov-Witten invariants of X. In this talk, I focus on the double cover of degree 8 determinantal surfaces in P^3, their non-Kahler small resolutions possessing Z_2 torsion, and their noncommutative resolutions. There is a derived equivalence between sheaves on the noncommutative resolutions and twisted sheaves on the small resolutions, suggesting a theory of Donaldson-Thomas invariants for these noncommutative resolutions.