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arXiv · 1405.5344

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

Hansol Hong·Hyung-Seok Shin
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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.

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Hansol Hong, Hyung-Seok Shin. 2014-06-15. On quantum cohomology ring of elliptic $\mathbb{P}^1$ orbifolds. https://arxiv.org/abs/1405.5344

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