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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2016
1. Verfasser: Ayano, T.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2016
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/147847
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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
id nasplib_isofts_kiev_ua-123456789-147847
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would like to thank Professor Shigeki Matsutani for answering a question on the paper [18] kindly and sending his unpublished paper.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.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
On Jacobi Inversion Formulae for Telescopic Curves
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On Jacobi Inversion Formulae for Telescopic Curves
spellingShingle On Jacobi Inversion Formulae for Telescopic Curves
Ayano, T.
title_short 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_sort on jacobi inversion formulae for telescopic curves
author Ayano, T.
author_facet Ayano, T.
publishDate 2016
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/147847
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.
work_keys_str_mv AT ayanot onjacobiinversionformulaefortelescopiccurves
first_indexed 2025-12-07T15:48:20Z
last_indexed 2025-12-07T15:48:20Z
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