# Maximal Degeneracy Points of GKZ Systems

@inproceedings{SHosono1996MaximalDP, title={Maximal Degeneracy Points of GKZ Systems}, author={S.Hosono and B.H.Lian and S.-T.Yau}, year={1996} }

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 for Calabi-Yau manifolds in mirror symmetry. We prove that for a suitable compactification of the parameter space, there exists certain special boundary points, which we called maximal degeneracy points, at which all but one solutions become singular.

## 8 Citations

On the better behaved version of the GKZ hypergeometric system

- Mathematics
- 2010

We consider a version of the generalized hypergeometric system introduced by Gelfand, Kapranov and Zelevinsky (GKZ) suited for the case when the underlying lattice is replaced by a finitely generated…

Period Integrals and the Riemann-Hilbert Correspondence

- Mathematics
- 2013

A tautological system, introduced in [16][17], arises as a regular holonomic system of partial differential equations that govern the period integrals of a family of complete intersections in a…

On the hyperplane conjecture for periods of Calabi–Yau hypersurfaces in $\mathbf{P}^n$

- Mathematics
- 2016

In [HLY1], Hosono, Lian, and Yau posed a conjecture characterizing the set of solutions to certain Gelfand-Kapranov-Zelevinsky hypergeometric equations which are realized as periods of Calabi-Yau…

Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system

- Mathematics
- 2012

We generalize the combinatorial description of the orbifold (Chen--Ruan) cohomology and of the Grothendieck ring of a Deligne--Mumford toric stack and its associated stacky fan in a lattice $N$ in…

Period integrals of CY and general type complete intersections

- Mathematics
- 2011

We develop a global Poincaré residue formula to study period integrals of families of complex manifolds. For any compact complex manifold X equipped with a linear system V∗ of generically smooth CY…

1 2 M ay 2 00 5 Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds

- Mathematics
- 2008

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…

Review of geometry and analysis

- Mathematics
- 2000

In this article, we shall discuss what the author considers to be important in geometry and related subjects. Since the time of the Greek mathematicians, geometry has always been in the center of…