Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds

Details Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds

1997-12-30

arxiv.org/abs/alg-geom/9712034v1

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, AMS-Latex. This is an extended version of the author's talk given during the Summer Symposium on Algebra at Universi

Scientific paper

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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