Genus two Gromov-Witten invariants of qunitic 3-folds

The programs and data in this page are for the following paper

        A Mirror Theorem for Genus Two Gromov-Witten invariant of Quintic 3-fold, arXiv:1709.07392, with Felix Janda and Yongbin Ruan.

First we consider the Picard-Fuchs equation and QDE for (λ,t)-equivariant theory defined in Lemma 3.6. to

• 1. Solve the Psi_{0,\alpha}-Matrix (step1)

  2. Solve the first row of the R-matrix R^*(z) 1 (step2)

  3. Solve R-matrix R^*(z) H^k for all k (step3)

where in the third step we only need to deal with t-equvariant theory. By the three steps we obtain the data for the R-matrix of t-equivariant theory.

Next, we compute the twisted invariants, they can be computed in terms of graph sums as in [GJR]. We finish the computation of the genus 2 formula in the following 3 steps:

• 1. Computing contribution0 of Γ^0 by using specialized S-matrices of t-twisted theory (proof of Proposition 2.7).

  2. Computing contribution2 of Γ^2 by using R-matrices of t-twisted theory (proof of Proposition 2.5).

  3. Computing contribution1 of Γ^1 by using both specialized S-matrices and R-matrices (proof of Proposition 2.6).