Huang, Klemm and Quackenbush computed the BPS invariants of the quintic 3-fold for low genera via the BCOV technique in http://arxiv.org/abs/hep-th/0612125. We can easily convert their data to get the GW invariants.
I think the bound is not a theorem, but an observation. We often assume such a vanishing condition to effectively solve the BCOV holomorphic anomaly equations.
Atsushi Kanazawa
- 675
- 1
- 4
- 9