Séminaire de géométrie algébrique

Navid Nabijou (Imperial college): Relative quasimaps and a quantum Lefschetz theorem

I 001 (Angers)

I 001


The theory of stable quasimaps is an important tool in modern enumerative geometry, providing an alternative system of curve counts to the usual Gromov-Witten invariants. In joint work with Luca Battistella, we define moduli spaces of relative stable quasimaps to a pair (X,Y), where Y is a hyperplane section in X. Intuitively these spaces parametrise quasimaps in X with specified orders of tangency with Y, and can be used to define relative quasimap invariants. By investigating these moduli spaces we obtain a quantum Lefschetz formula, expressing the quasimap invariants of Y in terms of the invariants of X. Since the I-function from mirror symmetry is equal to a generating function for these quasimap invariants, this result can be viewed as a “quantum Lefschetz theorem for I-functions.” It also agrees with an earlier formula obtained by Ciocan-Fontanine and Kim.