Counting of holomorphic orbi-spheres in (Formula presented) and determinant equations

Hansol Hong; Hyung Seok Shin

Counting of holomorphic orbi-spheres in (Formula presented) and determinant equations

Hansol Hong, Hyung Seok Shin

Department of Mathematics

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

Abstract

We count the number of holomorphic orbi-spheres in the ℤ₂-quotient of an elliptic curve. We first prove that there is an explicit correspondence between the holomorphic orbi-spheres and the sublet-tices of (formula presented). The problem of counting sublattices of index d then reduces to find the number of integer solutions of the equation αδ βγ = d up to an equivalence.

Original language	English
Pages (from-to)	603-629
Number of pages	27
Journal	New York Journal of Mathematics
Volume	23
Publication status	Published - 2017 May 31

Bibliographical note

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© 2017, University at Albany. All rights reserved.

All Science Journal Classification (ASJC) codes

Mathematics(all)

Cite this

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abstract = "We count the number of holomorphic orbi-spheres in the ℤ2-quotient of an elliptic curve. We first prove that there is an explicit correspondence between the holomorphic orbi-spheres and the sublet-tices of (formula presented). The problem of counting sublattices of index d then reduces to find the number of integer solutions of the equation αδ βγ = d up to an equivalence.",

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N2 - We count the number of holomorphic orbi-spheres in the ℤ2-quotient of an elliptic curve. We first prove that there is an explicit correspondence between the holomorphic orbi-spheres and the sublet-tices of (formula presented). The problem of counting sublattices of index d then reduces to find the number of integer solutions of the equation αδ βγ = d up to an equivalence.

AB - We count the number of holomorphic orbi-spheres in the ℤ2-quotient of an elliptic curve. We first prove that there is an explicit correspondence between the holomorphic orbi-spheres and the sublet-tices of (formula presented). The problem of counting sublattices of index d then reduces to find the number of integer solutions of the equation αδ βγ = d up to an equivalence.

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Counting of holomorphic orbi-spheres in (Formula presented) and determinant equations

Abstract

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