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International Mathematics Research Notices Advance Access published online on August 26, 2009
International Mathematics Research Notices, doi:10.1093/imrn/rnp135
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Sigma Function as A Tau Function

Atsushi Nakayashiki

Department of Mathematics, Kyushu University, Moto-Oka 744, Nishi-ku, Fukuoka 819-0395, Japan

Correspondence: Correspondence to be sent to: 6vertex{at}math.kyushu-u.ac.jp

The tau function corresponding to the affine ring of a certain plane algebraic curve, called (n, s)-curve, embedded in the universal Grassmann manifold is studied. It is neatly expressed by the multivariate sigma function. This expression is in turn used to prove fundamental properties on the series expansion of the sigma function established in a previous article in a different method.

Communicated by Prof. Igor Krichever


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