The Period map for quantum cohomology of ${\mathbb{P}}^2$

Abstract

We invert the period map defined by the second structure connection of quantum cohomology of ${\mathbb{P}}^2$. For small quantum cohomology the inverse is given explicitly in terms of the Eisenstein series $E_4$ and $E_6$, while for big quantum cohomology the inverse is determined perturbatively as a Taylor series expansion whose coefficients are quasi-modular forms.

58 pages. Typos fixed. The previous version was extended in the following way: we proved the Laplace transform version of the $\Gamma$-conjecture for ${\mathbb{P}}^2$, worked out the structure of a Schwarz triangular map, and added an appendix explaining the relation to vertex algebras and W-constraints. Version accepted in Adv. in Math

References in corpus (2)

• Gromov--Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda Hierarchies
• Lectures on Painleve property for semi-simple Frobenius manifolds

Cited by in corpus (3)

• Higher genera Catalan numbers and Hirota equations for extended nonlinear Schroedinger hierarchy
• Hirota Quadratic Equations for the Gromov--Witten Invariants of ${\mathbb{P}}_{n-2,2,2}^1$
• Reflection Vectors and Quantum Cohomology of Blowups