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Stable pair invariants of elliptically fibered Calabi-Yau threefolds and Jacobi forms

January 15, 2016 - 3:45pm
Stanford Mathematics department, room 383-N

In this talk, Sheldon Katz of UIUC will show the existence of certain global non-commutative structures on the moduli spaces of stable sheaves on algebraic varieties, whose formal completion at a closed point gives the pro-representable hull of the non-commutative deformation functor of the sheaf developed by Laudal, Eriksen, Segal and Efimov-Lunts-Orlov. He will then introduce the generating series through integrations over Hilbert schemes of points on these NC structures. When the underlying variety is a Calabi-Yau 3-fold, and the moduli space of stable sheaves satisfy some assumptions, this generating series admits a product expansion described by generalized DT invariants. This formula explains the dimension formula of Donovan-Wemyss’s contractions algebras for floppable curves on 3-folds in terms of genus zero Gopakumar-Vafa invariants.