On quantum cohomology ring of elliptic $\mathbb{P}^1$ orbifolds

Hansol Hong; Hyung-Seok Shin

On quantum cohomology ring of elliptic $\mathbb{P}^1$ orbifolds

Symplectic Geometry 2014-06-17 v2 Number Theory

Authors: Hansol Hong , Hyung-Seok Shin

Abstract

We compute quantum cohomology ring of elliptic $\mathbb{P}^1$ orbifolds via orbi-curve counting. The main technique is the classification theorem which relates holomorphic orbi-curves with certain orbifold coverings. The countings of orbi-curves are related to the integer solutions of Diophantine equations. This reproduces the computation of Satake and Takahashi in the case of $\mathbb{P}^1_{3,3,3}$ via different method.

Keywords

quantum cohomology ring elliptic orbifolds orbi-curve counting classification theorem orbifold coverings Diophantine equations

Cite

@article{arxiv.1405.5344,
  title  = {On quantum cohomology ring of elliptic $\mathbb{P}^1$ orbifolds},
  author = {Hansol Hong and Hyung-Seok Shin},
  journal= {arXiv preprint arXiv:1405.5344},
  year   = {2014}
}

Comments

37 pages, 11 figures, comments are welcome, v2: change in introduction

On quantum cohomology ring of elliptic $\mathbb{P}^1$ orbifolds

Abstract

Keywords

Cite

Comments

Related papers