Dualizing, projecting, and restricting GKZ systems

Maximal Degeneracy Points of Gkz Systems

Motivated by mirror symmetry, we study certain integral repre-sentations of solutions to the Gel′fand-Kapranov-Zelevinsky (GKZ) hypergeo-metric system. Some of these solutions arise as period integrals for Calabi-Yaumanifolds in mirror symmetry. We prove that for a suitable compactificationof the parameter space, there exist certain special boundary points, whichwe called ma...

Gkz Hypergeometric Systems and Applications to Mirror Symmetry

Mirror symmetry of Calabi-Yau manifolds is one of the most beautiful aspects of string theory. It has been applied with great success to do non-perturbative calculation of quantum cohomology rings1−10. More recently, new ideas have been developed to apply mirror symmetry to study the moduli space of the type II string vacua compactified on a Calabi-Yau manifold. Some of the recent work on verif...

Dualizing Complexes

Recognizing Dualizing Complexes

Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. This paper proves that M is a dualizing complex for A if and only if the trivial extension A ⋉M is a Gorenstein Differential Graded Algebra. As a corollary follows that A has a dualizing complex if and only if it is a quotient of a Gorenstein local Differential Graded Algebra. Let A be a noetherian local ...

On Matlis Dualizing Modules

We consider rings admitting a Matlis dualizing module E. We argue that if R admits two such dualizing modules, then a module is reflexive with respect to one if and only if it is reflexive with respect to the other. Using this fact we argue that the number (whether finite or infinite) of distinct dualizing modules equals the number of distinct invertible (R,R)-bimodules. We show by example that...