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June 2016 Holomorphic orbispheres in elliptic curve quotients and Diophantine equations
Hansol Hong, Hyung-Seok Shin
Kyoto J. Math. 56(2): 197-242 (June 2016). DOI: 10.1215/21562261-3478871

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 P3,3,31 via a different method.

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Hansol Hong. Hyung-Seok Shin. "Holomorphic orbispheres in elliptic curve quotients and Diophantine equations." Kyoto J. Math. 56 (2) 197 - 242, June 2016. https://doi.org/10.1215/21562261-3478871

Information

Received: 5 January 2015; Revised: 19 January 2015; Accepted: 28 January 2015; Published: June 2016
First available in Project Euclid: 10 May 2016

zbMATH: 1343.53087
MathSciNet: MR3500841
Digital Object Identifier: 10.1215/21562261-3478871

Subjects:
Primary: 53D45
Secondary: 11D45, 57R18

Rights: Copyright © 2016 Kyoto University

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Vol.56 • No. 2 • June 2016
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