Holomorphic orbispheres in elliptic curve quotients and Diophantine equations

Hansol Hong, Hyung Seok Shin

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Abstract

We compute quantum cohomology rings of elliptic P1 orbifolds via orbicurve counting. The main technique is the classification theorem which relates holomorphic orbicurves with certain orbifold coverings. The countings of orbicurves are related to the integer solutions of Diophantine equations. This reproduces the computation of Satake and Takahashi in the case of P13 ,3,3 via a different method.

Original languageEnglish
Pages (from-to)197-242
Number of pages46
JournalKyoto Journal of Mathematics
Volume56
Issue number2
DOIs
Publication statusPublished - 2016 Jun

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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