Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians

Victor V. Batyrev; Ionunt Ciocan-Fontanine; Bumsig Kim; Duco van Straten

doi:10.1016/s0550-3213(98)00020-0

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arXiv · alg-geom/9710022

Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians

Victor V. Batyrev·Ionunt Ciocan-Fontanine·Bumsig Kim·Duco van Straten

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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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Victor V. Batyrev, Ionunt Ciocan-Fontanine, Bumsig Kim, Duco van Straten. 1997-10-19. Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians. https://doi.org/10.1016/s0550-3213(98)00020-0

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