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April 2014 Sigma functions for telescopic curves
Takanori Ayano
Osaka J. Math. 51(2): 459-481 (April 2014).

Abstract

In this paper we consider a symplectic basis of the first cohomology group and the sigma functions for algebraic curves expressed by a canonical form using a finite sequence $(a_{1}, \ldots, a_{t})$ of positive integers whose greatest common divisor is equal to one (Miura [13]). The idea is to express a non-singular algebraic curve by affine equations of $t$ variables whose orders at infinity are $(a_{1}, \ldots, a_{t})$. We construct a symplectic basis of the first cohomology group and the sigma functions for telescopic curves, i.e., the curves such that the number of defining equations is exactly $t-1$ in the Miura canonical form. The largest class of curves for which such construction has been obtained thus far is $(n, s)$-curves ([4] [15]), which are telescopic because they are expressed in the Miura canonical form with $t=2$, $a_{1}=n$, and $a_{2}=s$, and the number of defining equations is one.

Citation

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Takanori Ayano. "Sigma functions for telescopic curves." Osaka J. Math. 51 (2) 459 - 481, April 2014.

Information

Published: April 2014
First available in Project Euclid: 8 April 2014

zbMATH: 1328.14057
MathSciNet: MR3192551

Subjects:
Primary: 14H55
Secondary: 14H42 , 14H50

Rights: Copyright © 2014 Osaka University and Osaka City University, Departments of Mathematics

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Vol.51 • No. 2 • April 2014
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