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

Hansol Hong, Hyung Seok Shin

Research output: Contribution to journalArticle

Abstract

We count the number of holomorphic orbi-spheres in the ℤ 2 -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 languageEnglish
Pages (from-to)603-629
Number of pages27
JournalNew York Journal of Mathematics
Volume23
Publication statusPublished - 2017 May 31

Fingerprint

Counting
Determinant
Elliptic Curves
Count
Quotient
Correspondence
Equivalence
Integer

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Counting of holomorphic orbi-spheres in (Formula presented) and determinant equations. / Hong, Hansol; Shin, Hyung Seok.

In: New York Journal of Mathematics, Vol. 23, 31.05.2017, p. 603-629.

Research output: Contribution to journalArticle

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