• Corpus ID: 119585579

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}
}
  • R. P. Horja
  • Published 14 December 1999
  • Mathematics
  • arXiv: Algebraic Geometry
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… 

Figures from this paper

Mirror symmetry: monodromy and autoequivalences of the derived category

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

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

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

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

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

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

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

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

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

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
...

References

SHOWING 1-10 OF 75 REFERENCES

Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties

We propose a combinatorical duality for lattice polyhedra which conjecturally gives rise to the pairs of mirror symmetric families of Calabi-Yau complete intersections in toric Fano varieties with

Categorical Mirror Symmetry: The Elliptic Curve

We describe an isomorphism of categories conjectured by Kontsevich. If M and f M are mirror pairs then the conjectural equivalence is between the derived category of coherent sheaves on M and a

Dual Cones and Mirror Symmetry for Generalized Calabi-Yau Manifolds

We introduce a special class of convex rational polyhedral cones which allows to construct generalized Calabi-Yau varieties of dimension $(d + 2(r-1))$, where $r$ is a positive integer and d is the

Maximal degeneracy points of GKZ systems

Motivated by mirror symmetry, we study certain integral representations of solutions to the Gel’fand-Kapranov-Zelevinsky(GKZ) hypergeometric system. Some of these solutions arise as period integrals

Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces

Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for

Duality in {Calabi-Yau} Moduli Space

Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties

We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV1,...,Vr in a toric

The monomial-divisor mirror map

For each family of Calabi-Yau hypersurfaces in toric varieties, Batyrev has proposed a possible mirror partner (which is also a family of Calabi-Yau hypersurfaces). We explain a natural construction

Homological Algebra of Mirror Symmetry

Mirror symmetry (MS) was discovered several years ago in string theory as a duality between families of 3-dimensional Calabi-Yau manifolds (more precisely, complex algebraic manifolds possessing
...