On Jacobi Inversion Formulae for Telescopic Curves
For a hyperelliptic curve of genus g, it is well known that the symmetric products of g points on the curve are expressed in terms of their Abel-Jacobi image by the hyperelliptic sigma function (Jacobi inversion formulae). Matsutani and Previato gave a natural generalization of the formulae to the m...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147847 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Jacobi Inversion Formulae for Telescopic Curves / A. Ayano // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862680933016010752 |
|---|---|
| author | Ayano, T. |
| author_facet | Ayano, T. |
| citation_txt | On Jacobi Inversion Formulae for Telescopic Curves / A. Ayano // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For a hyperelliptic curve of genus g, it is well known that the symmetric products of g points on the curve are expressed in terms of their Abel-Jacobi image by the hyperelliptic sigma function (Jacobi inversion formulae). Matsutani and Previato gave a natural generalization of the formulae to the more general algebraic curves defined by yr=f(x), which are special cases of (n,s) curves, and derived new vanishing properties of the sigma function of the curves yr=f(x). In this paper we extend the formulae to the telescopic curves proposed by Miura and derive new vanishing properties of the sigma function of telescopic curves. The telescopic curves contain the (n,s) curves as special cases.
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| first_indexed | 2025-12-07T15:48:20Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147847 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:48:20Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ayano, T. 2019-02-16T09:15:31Z 2019-02-16T09:15:31Z 2016 On Jacobi Inversion Formulae for Telescopic Curves / A. Ayano // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14H42; 14H50; 14H55 DOI:10.3842/SIGMA.2016.086 https://nasplib.isofts.kiev.ua/handle/123456789/147847 For a hyperelliptic curve of genus g, it is well known that the symmetric products of g points on the curve are expressed in terms of their Abel-Jacobi image by the hyperelliptic sigma function (Jacobi inversion formulae). Matsutani and Previato gave a natural generalization of the formulae to the more general algebraic curves defined by yr=f(x), which are special cases of (n,s) curves, and derived new vanishing properties of the sigma function of the curves yr=f(x). In this paper we extend the formulae to the telescopic curves proposed by Miura and derive new vanishing properties of the sigma function of telescopic curves. The telescopic curves contain the (n,s) curves as special cases. The author would like to thank Professor Shigeki Matsutani for answering a question on the
 paper [18] kindly and sending his unpublished paper. The author would like to thank Professor
 Atsushi Nakayashiki for inviting him the conference “Curves, Moduli and Integrable Systems”
 at Tsuda College and giving valuable discussions. The author would like to thank Professor
 Masato Okado for the support of travel costs for a presentation at Tsukuba University. The
 author would like to thank Professor Yoshihiro Onishi for inviting him Meijo University and
 giving valuable discussions. The author would like to thank the anonymous referees for reading
 our paper carefully and giving many valuable comments. In particular, the author is deeply
 grateful for their warm encouragement. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Jacobi Inversion Formulae for Telescopic Curves Article published earlier |
| spellingShingle | On Jacobi Inversion Formulae for Telescopic Curves Ayano, T. |
| title | On Jacobi Inversion Formulae for Telescopic Curves |
| title_full | On Jacobi Inversion Formulae for Telescopic Curves |
| title_fullStr | On Jacobi Inversion Formulae for Telescopic Curves |
| title_full_unstemmed | On Jacobi Inversion Formulae for Telescopic Curves |
| title_short | On Jacobi Inversion Formulae for Telescopic Curves |
| title_sort | on jacobi inversion formulae for telescopic curves |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147847 |
| work_keys_str_mv | AT ayanot onjacobiinversionformulaefortelescopiccurves |