Appears in collection : Maxim Kontsevich : Birational Invariants from Gromov-Witten Theory

Gromov-Witten invariants of a smooth projective variety give an infinite tower of cohomology classes on powers of the original variety, satisfying a beautiful system of constraints encoded in the notion of quantum connection. Recently Hiroshi Iritani proved a result controlling the quantum connection of the blowup along a smooth center. The goal of the course is to introduce a new class of birational invariants based on Iritani's theorem. In particular, one can almost effortlessly prove the non-rationality of a generic cubic 4-fold.