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Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds

Victor V. Batyrev
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Abstract

For an arbitrary smooth n-dimensional Fano variety $X$ we introduce the notion of a small toric degeneration. Using small toric degenerations of Fano n-folds $X$, we propose a general method for constructing mirrors of Calabi-Yau complete intersections in $X$. Our mirror construction is based on a generalized monomial-divisor mirror correspondence which can be used for computing Gromov-Witten invariants of rational curves via specializations of GKZ-hypergeometric series.

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BibTeXRIS

Victor V. Batyrev. 1997-12-30. Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds. https://arxiv.org/abs/alg-geom/9712034

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