Asian Journal of Mathematics

Volume 14 (2010)

Number 2

On Algebraic Expressions of Sigma Functions for (n, s) Curves

Pages: 175 – 212

DOI: http://dx.doi.org/10.4310/AJM.2010.v14.n2.a2

Author

Atsushi Nakayashiki

Abstract

An expression of the multivariate sigma function associated with an (n,s)-curve is given in terms of algebraic integrals. As a corollary the first term of the series expansion around the origin of the sigma function is directly proved to be Schur function determined from the gap sequence at infinity.

Keywords

Sigma Function; Schur function; gap sequence

2010 Mathematics Subject Classification

14H42, 14H55, 14H70

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