2018/02/02 by Boris Dubrovin, Di Yang, Dubrovin, Boris +3 · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1802.00711
A conjectural formula for the k-point generating function of Gromov--Witten invariants of the Riemann sphere for all genera and all degrees was proposed in \citeDY2. In this paper, we give a proof of this formula together with an explicit analytic (as opposed to formal) expression for the corresponding matrix resolvent. We also give a formula for the k-point function as a sum of (k-1)! products of hypergeometric functions of one variable. We show that the k-point generating function coincides with the ε→ 0 asymptotics of the analytic k-point function, and also compute three more asymptotics of the analytic function for ε→ ∞, q→ 0, q→∞, thus defining new invariants for the Riemann sphere.