Kodaira-Spencer maps for elliptic orbispheres as isomorphisms of Frobenius algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914947904045056 |
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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 |