| Résume | Gromov-Witten invariants of a projective variety X come from enumerating curves in X. A famous example for X is the quintic hypersurface in P^4, studied by string theorists regarding mirror symmetry. Invariants from genus zero curves into X have been computed out of invariants of P^4, following the so-called quantum Lefschetz principle. However, invariants from higher genus curves are much harder to compute. In particular, based on a specific example, one may believe that they cannot be deduced from invariants of the ambient space P^4. In this talk, I will present a conjectural relation to the ambient space, I will show where it comes from and a possible road to proving it. |
