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Quantum Serre duality for quasimaps
Levi Heath, Mark Shoemaker
Let be a smooth variety or orbifold and let be a complete intersection defined by a section of a vector bundle . Originally proposed by Givental, quant…
Extremal transitions via quantum Serre duality
Rongxiao Mi, Mark Shoemaker
Two varieties and are said to be related by extremal transition if there exists a degeneration from to a singular variety and a crepant resolut…
Virtual classes for hypersurfaces via two-periodic complexes
Mark Shoemaker
These expository notes are based on a series of lectures given at the May 2018 Snowbird workshop, Crossing the Walls in Enumerative Geometry. We give an introductory treatment of t…
Narrow quantum D-modules and quantum Serre duality
Mark Shoemaker
Given Y a non-compact manifold or orbifold, we define a natural subspace of the cohomology of Y called the narrow cohomology. We show that despite Y being non-compact, there is a w…
Integral transforms and quantum correspondences
Mark Shoemaker
We reframe a collection of well-known comparison results in genus zero Gromov-Witten theory in order to relate these to integral transforms between derived categories. This implies…
Fundamental Factorization of a GLSM, Part I: Construction
Ionut Ciocan-Fontanine, David Favero, Jérémy Guéré +2
We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases, these invariants recover both the Gromov-Witten type…