Reflection Vectors and Quantum Cohomology of Blowups

Todor Milanov ; Xiaokun Xia

Symmetry, integrability and geometry: methods and applications, Tome 20 (2024)

Résumé

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 reflection group. 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.

Détail

Keywords: Gromov–Witten invariants; quantum cohomology.
Mots-clés : Frobenius structures

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