Holomorphic orbispheres in elliptic curve quotients and Diophantine equations

Hansol Hong; Hyung Seok Shin

doi:10.1215/21562261-3478871

Holomorphic orbispheres in elliptic curve quotients and Diophantine equations

Hansol Hong, Hyung Seok Shin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 P¹_{3 ,3,3} via a different method.

Original language	English
Pages (from-to)	197-242
Number of pages	46
Journal	Kyoto Journal of Mathematics
Volume	56
Issue number	2
DOIs	https://doi.org/10.1215/21562261-3478871
Publication status	Published - 2016 Jun

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© 2016 by Kyoto University.

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1215/21562261-3478871

Cite this

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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.",

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AB - 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.

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Holomorphic orbispheres in elliptic curve quotients and Diophantine equations

Abstract

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