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On Jacobi Inversion Formulae for Telescopic Curves
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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On Jacobi Inversion Formulae for Telescopic Curves
Інший ID:
2010 Mathematics Subject Classification: 14H42; 14H50; 14H55
DOI:10.3842/SIGMA.2016.086
DOI:10.3842/SIGMA.2016.086
Посилання:
On Jacobi Inversion Formulae for Telescopic Curves / A. Ayano // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ.
Підтримка:
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paper [18] kindly and sending his unpublished paper.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.
Дата:
2016
Переглядів:
497
Завантажень:
272
Анотація:
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.
