Kodaira-Spencer maps for elliptic orbispheres as isomorphisms of Frobenius algebras

Fuente: arXiv
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Main Author: Lee, Sangwook
Format: Preprint
Published: 2024
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author Lee, Sangwook
author_facet Lee, Sangwook
contents Given a mirror pair of a symplectic manifold $X$ and a Landau-Ginzburg potential $W$, we are interested in the problem whether the quantum cohomology of $X$ and the Jacobian algebra of $W$ are isomorphic. Since those can be equipped with Frobenius algebra structures, we might ask whether they are isomorphic as Frobenius algebras. We show that the Kodaira-Spencer map gives a Frobenius algebra isomorphism for elliptic orbispheres, under the Floer theoretic modification of the residue pairing.
format Preprint
id arxiv_https___arxiv_org_abs_2409_07814
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Kodaira-Spencer maps for elliptic orbispheres as isomorphisms of Frobenius algebras
Lee, Sangwook
Symplectic Geometry
Given a mirror pair of a symplectic manifold $X$ and a Landau-Ginzburg potential $W$, we are interested in the problem whether the quantum cohomology of $X$ and the Jacobian algebra of $W$ are isomorphic. Since those can be equipped with Frobenius algebra structures, we might ask whether they are isomorphic as Frobenius algebras. We show that the Kodaira-Spencer map gives a Frobenius algebra isomorphism for elliptic orbispheres, under the Floer theoretic modification of the residue pairing.
title Kodaira-Spencer maps for elliptic orbispheres as isomorphisms of Frobenius algebras
topic Symplectic Geometry
url https://arxiv.org/abs/2409.07814