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Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians
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abstract
In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of rational curves on complete intersection Calabi-Yau 3-folds in Grassmannians. Using a natural degeneration of Grassmannians $G(k,n)$ to some Gorenstein toric Fano varieties $P(k,n)$ with conifolds singularities which was recently described by Sturmfels, we suggest an explicit mirror construction for Calabi-Yau complete intersections $X \subset G(k,n)$ of arbitrary dimension. Our mirror construction is consistent with the formula for the Lax operator conjectured by Eguchi, Hori and Xiong for gravitational quantum cohomology of Grassmannians.
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A single point as a Calabi-Yau zerofold
A single point is realized as the large-volume phase of a non-abelian GLSM, with a non-regular other phase, divergent partition function sums, and a matching mirror period.
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