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arXiv · 2304.04365

Reflection Vectors and Quantum Cohomology of Blowups

Todor Milanov·Xiaokun Xia
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Abstract

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.

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Todor Milanov, Xiaokun Xia. 2023-04-10. Reflection Vectors and Quantum Cohomology of Blowups. https://doi.org/10.3842/sigma.2024.029

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