## Generalized Hypergeometric Functions and Rational Curves on Calabi-Yau complete intersections in Toric Varieties (1995)

Venue: | COMMUN. MATH. PHYS |

Citations: | 75 - 14 self |

### BibTeX

@ARTICLE{Batyrev95generalizedhypergeometric,

author = {Victor V. Batyrev and Duco Van Straten},

title = { Generalized Hypergeometric Functions and Rational Curves on Calabi-Yau complete intersections in Toric Varieties},

journal = {COMMUN. MATH. PHYS},

year = {1995},

pages = {493--533}

}

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### Abstract

We formulate general conjectures about the relationship between the A-model connection on the cohomology of a d-dimensional Calabi-Yau complete intersection V of r hypersurfaces V1,...,Vr in a toric variety PΣ and the system of differential operators annihilating the special generalized hypergeometric function Φ0 depending on the fan Σ. In this context, the mirror symmetry phenomenon can be interpreted as the twofold characterization of the series Φ0. First, Φ0 is defined by intersection numbers of rational curves in PΣ with the hypersurfaces Vi and their toric degenerations. Second, Φ0 is the power expansion near a boundary point of the moduli space of the monodromy invariant period of the homolomorphic differential d-form on an another Calabi-Yau d-fold V ′ called the mirror of V. Using this generalized hypergeometric series, we propose a general construction for mirrors V ′ of V and canonical q-coordinates on the moduli spaces of Calabi-Yau manifolds.