Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds

Victor V. Batyrev

Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds

alg-geom 2007-05-23 v1 High Energy Physics - Theory Algebraic Geometry

Authors: Victor V. Batyrev

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.

Keywords

Fano variety toric degeneration mirror manifold Gromov-Witten invariant GKZ hypergeometric series

Cite

@article{arxiv.alg-geom/9712034,
  title  = {Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds},
  author = {Victor V. Batyrev},
  journal= {arXiv preprint arXiv:alg-geom/9712034},
  year   = {2007}
}

Comments

13 pages, AMS-Latex. This is an extended version of the author's talk given during the Summer Symposium on Algebra at University of Niigata, July 22-25, 1997

Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds

Abstract

Keywords

Cite

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