Weyl symmetry for curve counting invariants via spherical twists

Abstract: Abstract: Let X be a Calabi-Yau 3-fold containing a ruled surface W and let B be the homology class of the lines in the ruling. Physics suggests that curve counting on X should satisfy some symmetry relating curves in classes β and β’=β+(W.β)B. In this talk I’ll explain how to make such a symmetry precise with a new rationality result for the Pandharipande-Thomas invariants of X. Mathematically, the symmetry is explained by a certain involution of the derived category of X constructed using a particular spherical functor; our proof is an instance of the general principle that automorphisms of the derived category should constrain enumerative invariants. This is joint work with Tim Buelles and it is highly inspired in the proof of rationality for the PT generating series of an orbifold by Beentjes-Calabrese-Rennemo.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Comments: Zoom Meeting ID: 271 534 5558 Passcode: YMSC

Events Hub: Enumerative geometry