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

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 ${\mathbb{P}}_{3,3,3}^1$ via different method.

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

References in corpus (2)

• Gromov-Witten theory of elliptic orbifold P^1 and quasi-modular forms
• Landau-Ginzburg/Calabi-Yau Correspondence of all Genera for Elliptic Orbifold $p^1$