New York Journal of Mathematics
Volume 23 (2017) 603-629


Hansol Hong and Hyung-Seok Shin

Counting of holomorphic orbi-spheres in P12,2,2,2 and determinant equations

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Published: May 31, 2017
Keywords: Orbifold Gromov-Witten theory, Elliptic quotients
Subject: 53D45, 57R18

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 sublattices of ZZ \sqrt{-1} (⊂ C). The problem of counting sublattices of index d then reduces to find the number of integer solutions of the equation α δ - β γ = d up to an equivalence.


The work of H. Hong described in this paper was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK2130405 and CUHK2130446).

Author information

Hansol Hong:
Center of Mathematical Sciences and Applications, Harvard University, 20, Garden Street, Cambridge, MA 02138

Hyung-Seok Shin:
School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro Dongdaemun-gu, Seoul 02455, Republic of Korea