Open Access
October, 2008 Jacobi inversion on strata of the Jacobian of the C rs curve y r =f(x)
Shigeki MATSUTANI, Emma PREVIATO
J. Math. Soc. Japan 60(4): 1009-1044 (October, 2008). DOI: 10.2969/jmsj/06041009

Abstract

By using the generalized sigma function of a C rs curve y r =f(x) , we give a solution to the Jacobi inversion problem over the stratification in the Jacobian given by the Abel image of the symmetric products of the curve. We show that determinants consisting of algebraic functions on the curve, whose zeros give the Abelian pre-image of the strata, are written by ratios of certain derivatives of the sigma function on the strata. We also discuss the order of vanishing of abelian functions on the strata in terms of intersection theory.

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Shigeki MATSUTANI. Emma PREVIATO. "Jacobi inversion on strata of the Jacobian of the C rs curve y r =f(x) ." J. Math. Soc. Japan 60 (4) 1009 - 1044, October, 2008. https://doi.org/10.2969/jmsj/06041009

Information

Published: October, 2008
First available in Project Euclid: 5 November 2008

zbMATH: 1160.14018
MathSciNet: MR2467868
Digital Object Identifier: 10.2969/jmsj/06041009

Subjects:
Primary: 14H40
Secondary: 14H55 , 14H70 , 14K20

Keywords: $C_{ab}$ curve , inversion of abelian integrals , Sigma Function

Rights: Copyright © 2008 Mathematical Society of Japan

Vol.60 • No. 4 • October, 2008
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