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1) Apparently, physicist can calculate the GW invariants of quintic CY 3-fold up to genus 51. I am looking for a reference that has a table of these number for some low degrees (say up to degree 5) and low genera (at least until g=3).

2) For each genus g, there is a lower bound $d(g)$ such that for every $d<d(g)$, all genus g degree d invariants of quintic are zero. Where can I found this lower bound?

Thanks.

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up vote 3 down vote accepted

1) 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.

2) 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.

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