Todor Milanov:Reflection vectors and quantum cohomology of blowups

Abstract: Let X be a smooth projective variety with a semi-simple quantum cohomology. The monodromy group of the quantum cohomology is by definition the monodromy group of the so-called second structure connection. There is a very interesting conjecture, more or less equivalent to Dubrovin's conjecture, that gives an explicit description of the monodromy group in terms of the exceptional objects of the derived category of X. In a joint work with my student Xiaokun Xia, we made an interesting progress in proving that the conjectural description of the monodromy group is compatible with the operation of blowing up at finitely many points. More precisely, we proved that the exceptional objects in Orlov's full exceptional collection of the blowup Bl(X) that are supported on the exceptional divisor are reflection vectors.