Quantum Modules of Semipositive Toric Varieties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929615278178304 |
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| author | Lee, Jae Hwang |
| author_facet | Lee, Jae Hwang |
| contents | A smooth projective toric variety $X=X_Σ$ has a geometric quotient description $V /\!/ T$. Using $2|1$-pointed quasimap invariants, one can define a quantum $H^*(T)$-module $QM(X)$, which deforms a natural module structure given by the Kirwan map $H^*(T) \rightarrow H^*(X)$. The Batyrev ring of $X$, defined from combinatorial data of the fan $Σ$, has its natural module structure given by the quotient of a polynomial ring, say BatM$(X)$. In this paper, we prove that $QM(X)$ and BatM$(X)$ are naturally isomorphic when $X$ is semipositive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03273 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Modules of Semipositive Toric Varieties Lee, Jae Hwang Algebraic Geometry 14N35, 53D45 A smooth projective toric variety $X=X_Σ$ has a geometric quotient description $V /\!/ T$. Using $2|1$-pointed quasimap invariants, one can define a quantum $H^*(T)$-module $QM(X)$, which deforms a natural module structure given by the Kirwan map $H^*(T) \rightarrow H^*(X)$. The Batyrev ring of $X$, defined from combinatorial data of the fan $Σ$, has its natural module structure given by the quotient of a polynomial ring, say BatM$(X)$. In this paper, we prove that $QM(X)$ and BatM$(X)$ are naturally isomorphic when $X$ is semipositive. |
| title | Quantum Modules of Semipositive Toric Varieties |
| topic | Algebraic Geometry 14N35, 53D45 |
| url | https://arxiv.org/abs/2412.03273 |