# Hypergeometric functions and mirror symmetry in toric varieties

@article{Horja1999HypergeometricFA, title={Hypergeometric functions and mirror symmetry in toric varieties}, author={Richard Paul Horja}, journal={arXiv: Algebraic Geometry}, year={1999} }

We study aspects related to Kontsevich's homological mirror symmetry conjecture in the case of Calabi-Yau complete intersections in toric varieties. In a 1996 lecture at Rutgers University, Kontsevich indicated how his proposal implies that the groups of automorphisms of the two types of categories involved in the homological mirror symmetry conjecture should also be identified. Our main results provide an explicit geometric construction of the correspondence between the automorphisms of the…

## 120 Citations

### Mirror symmetry: monodromy and autoequivalences of the derived category

- Mathematics
- 2020

For mirror symmetric families of (weak) Calabi-Yau varieties we study a conjecture of Kontsevich on the relation between the monodromy of one family and the action on cohomology of the group of…

### Local mirror symmetry and type IIA monodromy of Calabi-Yau manifolds

- Mathematics
- 2000

We propose a monodromy invariant pairing Khol(X) H3(X _ ;Z) ! Q for a mirror pair of Calabi-Yau manifolds, (X; X _ ). This pairing is utilized implicitly in the previous calculations of the…

### Diffeomorphisms and Families of Fourier-Mukai Transforms in Mirror Symmetry

- Mathematics
- 2001

Assuming the standard framework of mirror symmetry, a conjecture is formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y should act by families of Fourier-Mukai transforms…

### Neron-Severi Lie algebra, autoequivalences of the derived category, and monodromy

- Mathematics
- 2020

This preprint supersedes the previous version, which was only about Kontsevich's conjecture on the relation between the monodromy of a family of (weakly) CY varieties and the action on cohomology of…

### Central charges, symplectic forms, and hypergeometric series in local mirror symmetry

- Mathematics
- 2004

We study a cohomology-valued hypergeometric series which naturally arises in the description of (local) mirror symmetry. We identify it as a central charge formula for BPS states and study its…

### Derived category automorphisms from mirror symmetry

- Mathematics
- 2001

Inspired by the homological mirror symmetry conjecture of Kontsevich [30], we construct new classes of automorphisms of the bounded derived category of coherent sheaves on a smooth quasi– projective…

### Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds

- Mathematics
- 2005

This proceedings note introduces aspects of the authors' work relating mirror symmetry and integral variations of Hodge structure. The emphasis is on their classification of the integral variations…

### Monodromy at infinity of A-hypergeometric functions and toric compactifications

- Mathematics
- 2008

We study non-confluent A-hypergeometric systems introduced by Gelfand et al. (Funct Anal Appl 23:94–106, 1989) and prove a formula for the eigenvalues of their monodromy automorphisms defined by the…

### Invariants of hypergeometric groups for Calabi-Yau complete intersections in weighted projective spaces

- Mathematics
- 2013

Let Y be a Calabi-Yau complete intersection in a weighted projective space. We show that the space of quadratic invariants of the hypergeometric group associated with the twisted I-function is…

### Autoequivalences of derived category of a K3 surface and monodromy transformations

- Mathematics
- 2002

We consider autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. We prove that the image of the autoequivalences has index at most two in the group of the Hodge…

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- Mathematics
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- Mathematics
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- Mathematics
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