This article is cited in 5 papers

On Addition Formulae for Sigma Functions of Telescopic Curves

Takanori Ayano^a, Atsushi Nakayashiki<sup>b

a</sup> Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan
^b Department of Mathematics, Tsuda College, Kodaira, Tokyo 187-8577, Japan

Abstract: A telescopic curve is a certain algebraic curve defined by $m-1$ equations in the affine space of dimension $m$, which can be a hyperelliptic curve and an $(n,s)$ curve as a special case. We extend the addition formulae for sigma functions of $(n,s)$ curves to those of telescopic curves. The expression of the prime form in terms of the derivative of the sigma function is also given.

Keywords: sigma function; tau function; Schur function; Riemann surface; telescopic curve; gap sequence.

MSC: 14H70; 37K20; 14H55; 14K25

Received: March 13, 2013; in final form June 14, 2013; Published online June 19, 2013

Language: English

DOI: 10.3842/SIGMA.2013.046

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ArXiv: 1303.2878