Reflection Vectors and Quantum Cohomology of Blowups

Abstract

Let $X$ be a smooth projective variety with a semisimple quantum cohomology. It is known that the blowup ${\mathrm{Bl}}_{\mathrm{pt}}(X)$ of $X$ at one point also has semisimple quantum cohomology. In particular, the monodromy group of the quantum cohomology of ${\mathrm{Bl}}_{\mathrm{pt}}(X)$ is a reflectiongroup. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of ${\mathrm{Bl}}_{\mathrm{pt}}(X)$ depending only on the geometry of the exceptional divisor.

References in corpus (2)

• Degenerate Riemann-Hilbert-Birkhoff problems, semisimplicity, and convergence of WDVV-potentials
• The Period map for quantum cohomology of ${\mathbb{P}}^2$