Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 9 (2013), 046, 14 pages      arXiv:1303.2878      https://doi.org/10.3842/SIGMA.2013.046

On Addition Formulae for Sigma Functions of Telescopic Curves

Takanori Ayano a and Atsushi Nakayashiki b
a) Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan
b) Department of Mathematics, Tsuda College, Kodaira, Tokyo 187-8577, Japan

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

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.

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

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