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

Sangwook Lee

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arXiv · 2409.07814

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

Sangwook Lee

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Abstract

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.

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Sangwook Lee. 2024-09-12. Kodaira-Spencer maps for elliptic orbispheres as isomorphisms of Frobenius algebras. https://arxiv.org/abs/2409.07814

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