Harvard-MIT Algebraic Geometry Seminar

Tuesday, September 28, 2021 at 3:00pm to 4:00pm

Virtual Event

Zoom info available upon request. Email: maulik@mit.edu

Featured Speaker: Miguel Moreira (ETH Zurich)

Title: Weyl symmetry for curve counting invariants via spherical twists.

Let Y be a Calabi-Yau 3-fold containing a Hirzebruch surface E and let B be the homology class of the fibers of the Hirzebruch surface. Physics suggests that curve counting on Y should satisfy some symmetry relating curves in classes β and β’=β+(E.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 Y. Mathematically, the symmetry is explained by a certain involution of the derived category of Y given as a composition of spherical twists; 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.

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