On the Thomae formula for Z_N curves

1996/08/20 by Nakayashiki, Atsushi
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9608016

Abstract

We shall give an elementary and rigorous proof of the Thomae formula for \bf Z_N curves which was discovered by Bershadsky and Radul. Instead of using the determinant of the Laplacian we use the traditional variational method which goes back to Riemann, Thomae, Fuchs. In the proof we made explicit the algebraic expression of the chiral Szegö kernels and proves the vanishing of zero values of derivatives of theta functions with \bf Z_N invariant 1/2N characteristics.

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