LG/CY correspondence: the state space isomorphism

Details LG/CY correspondence: the state space isomorphism LG/CY correspondence: the state space isomorphism

2009-08-06

arxiv.org/abs/0908.0908v2

Mathematics

Algebraic Geometry

37 pages, 9 figures

Scientific paper

We prove the classical mirror symmetry conjecture for the mirror pairs constructed by Berglund, H\"ubsch, and Krawitz. Our main tool is a cohomological LG/CY correspondence which provides a degree-preserving isomorphism between the cohomology of finite quotients of Calabi-Yau hypersurfaces inside a weighted projective space and the Fan-Jarvis-Ruan-Witten state space of the associated Landau-Ginzburg singularity theory.

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