A mirror theorem for toric complete intersections
Alexander Givental (UC Berkeley)
TL;DR
This paper proves a generalized mirror theorem for toric complete intersections, expressing quantum cohomology solutions via hypergeometric functions, advancing the understanding of mirror symmetry in symplectic toric manifolds.
Contribution
It establishes a new mirror theorem for non-negative complete intersections in symplectic toric manifolds, linking quantum cohomology to hypergeometric functions.
Findings
Solutions of quantum cohomology PDEs are expressed in terms of hypergeometric functions.
The mirror conjecture is generalized to a broader class of toric complete intersections.
An error in the original introduction was corrected.
Abstract
We prove a generalized mirror conjecture for non-negative complete intersections in symplectic toric manifolds. Namely, we express solutions of the PDE system describing quantum cohomology of such a manifold in terms of suitable hypergeometric functions. Revision 03.03.97: we correct an error in Introduction.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Commutative Algebra and Its Applications · Topological and Geometric Data Analysis