English

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

Algebraic Geometry 2019-05-31 v2 High Energy Physics - Theory

Abstract

We invert the period map defined by the second structure connection of quantum cohomology of P2\mathbb{P}^2. For small quantum cohomology the inverse is given explicitly in terms of the Eisenstein series E4E_4 and E6E_6, while for big quantum cohomology the inverse is determined perturbatively as a Taylor series expansion whose coefficients are quasi-modular forms.

Keywords

Cite

@article{arxiv.1706.04323,
  title  = {The Period map for quantum cohomology of $\mathbb{P}^2$},
  author = {Todor Milanov},
  journal= {arXiv preprint arXiv:1706.04323},
  year   = {2019}
}

Comments

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