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Determinantal Calabi-Yau varieties in Grassmannians and the Givental \(I\)-functions. (English) Zbl 1405.83065

Summary: We examine a class of Calabi-Yau varieties of the determinantal type in Grassmannians and clarify what kind of examples can be constructed explicitly. We also demonstrate how to compute their genus-0 Gromov-Witten invariants from the analysis of the Givental \(I\)-functions. By constructing \(I\)-functions from the supersymmetric localization formula for the two dimensional gauged linear sigma models, we describe an algorithm to evaluate the genus-0 A-model correlation functions appropriately. We also check that our results for the Gromov-Witten invariants are consistent with previous results for known examples included in our construction.

MSC:

83E30 String and superstring theories in gravitational theory
81T45 Topological field theories in quantum mechanics
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
53Z05 Applications of differential geometry to physics
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