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Determinantal Calabi-Yau varieties in Grassmannians and the Givental $I$-functions

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arxiv 1810.03685 v1 pith:3RMKSLKW submitted 2018-10-08 hep-th math.AG

Yoshinori Honma , Masahide Manabe This is my paper · ORCID
classification hep-thmath.AG
keywords functionscalabi-yaudeterminantalexamplesgenus-0giventalgrassmanniansgromov-witten
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abstract

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.

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