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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.04365 |
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| _version_ | 1866917630294622208 |
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| author | Milanov, Todor Xia, Xiaokun |
| author_facet | Milanov, Todor Xia, Xiaokun |
| contents | Let $X$ be a smooth projective variety with a semisimple quantum cohomology. It is known that the blowup $\operatorname{Bl}_{\rm pt}(X)$ of $X$ at one point also has semisimple quantum cohomology. In particular, the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ is a reflectiongroup. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ depending only on the geometry of the exceptional divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_04365 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reflection Vectors and Quantum Cohomology of Blowups Milanov, Todor Xia, Xiaokun Algebraic Geometry 14N35, 35Q53 Let $X$ be a smooth projective variety with a semisimple quantum cohomology. It is known that the blowup $\operatorname{Bl}_{\rm pt}(X)$ of $X$ at one point also has semisimple quantum cohomology. In particular, the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ is a reflectiongroup. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of $\operatorname{Bl}_{\rm pt}(X)$ depending only on the geometry of the exceptional divisor. |
| title | Reflection Vectors and Quantum Cohomology of Blowups |
| topic | Algebraic Geometry 14N35, 35Q53 |
| url | https://arxiv.org/abs/2304.04365 |