Elsevier

Nuclear Physics B

Volume 514, Issue 3, 23 March 1998, Pages 640-666
Nuclear Physics B

Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians

https://doi.org/10.1016/S0550-3213(98)00020-0Get rights and content

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 ⊂ 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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