Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds

الأصل · EN

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.