Jacobi inversion on strata of the Jacobian of the $C_{rs}$ curve $y^r = f(x)$. II

Details Jacobi inversion on strata of the Jacobian of the $C_{rs}$ curve $y^r = f(x)$. II Jacobi inversion on strata of the Jacobian of the $C_{rs}$ curve $y^r = f(x)$. II

2010-06-06

arxiv.org/abs/1006.1090v4

Mathematics

Algebraic Geometry

31 pages

Scientific paper

Continuing previous work by the authors (J. Math. Soc. Japan 60 (2008) 1009-1044), this paper gives the precise order of vanishing of the $\sigma$-function on a stratification of the Jacobian of a cyclic $C_{rs}$ curve. The result is expressed through combinatorial properties of the Schur functions, related to the stratification of Sato's infinite-dimensional Grassmann manifold.

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