On Hyperelliptic Abelian Functions of Genus 3

Mathematics – Algebraic Geometry

Scientific paper

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40 pages

Scientific paper

The affine ring A of the affine Jacobian variety of a hyperelliptic curve of
genus 3 is studied as a D-module. The conjecture on the minimal D-free
resolution previously proposed is proved in this case. As a by-product a linear
basis of A is explicitly constructed in terms of derivatives of Klein's
hyperelliptic pe functions.

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