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 Blₚₜ(𝑋) of 𝑋 at one point also has semisimple quantum cohomology. In particular, the monodromy group of the quantum cohomology of Blₚₜ(𝑋) is a reflectiongroup. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of Blpt(𝑋) depending only on the geometry of the exceptional divisor.