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Differential Structure of Abelian Functions

K. Cho·A. Nakayashiki
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Abstract

The space of abelian functions of a principally polarized abelian variety J is studied as a module over the ring D of global holomorphic differential operators on J. We construct a D-free resolution in case the theta divisor is non-singular. As an application, in the case of dimension 2 and 3, we construct a new linear basis of the space of abelian functions in terms of logarithmic derivatives of the higher dimensional sigma function.

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K. Cho, A. Nakayashiki. 2006-04-12. Differential Structure of Abelian Functions. https://arxiv.org/abs/math/0604267

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