Comparison of Frobenius algebra structures on Calabi-Yau toric hypersurfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912318129963008 |
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| author | Park, Jeehoon Yoo, Philsang |
| author_facet | Park, Jeehoon Yoo, Philsang |
| contents | We establish an isomorphism between two Frobenius algebra structures, termed CY and LG, on the primitive cohomology of a smooth Calabi--Yau hypersurface in a simplicial Gorenstein toric Fano variety. As an application of our comparison isomorphism, we observe the existence of a Frobenius manifold structure on a finite-dimensional subalgebra of the Jacobian algebra of a homogeneous polynomial which may exhibit a non-compact singularity locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06694 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparison of Frobenius algebra structures on Calabi-Yau toric hypersurfaces Park, Jeehoon Yoo, Philsang Algebraic Geometry Mathematical Physics 14J32, 32S25, 14F25 We establish an isomorphism between two Frobenius algebra structures, termed CY and LG, on the primitive cohomology of a smooth Calabi--Yau hypersurface in a simplicial Gorenstein toric Fano variety. As an application of our comparison isomorphism, we observe the existence of a Frobenius manifold structure on a finite-dimensional subalgebra of the Jacobian algebra of a homogeneous polynomial which may exhibit a non-compact singularity locus. |
| title | Comparison of Frobenius algebra structures on Calabi-Yau toric hypersurfaces |
| topic | Algebraic Geometry Mathematical Physics 14J32, 32S25, 14F25 |
| url | https://arxiv.org/abs/2504.06694 |