Absolute vs. relative Gromov-Witten invariants

We compare absolute and relative Gromov-Witten invariants with the basic contact vector for very positive divisors. For such divisors, one might expect that these invariants are the same up to a natural multiple. We show that this is indeed the case outside of a narrow range of the dimension of the target and the genus of the domain. We provide explicit examples to show that these invariants are generally different inside of this range. This is joint work with A. Zinger.