Differential structure of Abelian functions

Koji Cho, Atsushi Nakayashiki

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The space of Abelian functions of a principally polarized abelian variety (J,Θ) is studied as a module over the ring D of global holomorphic differential operators on J. We construct a D free resolution in case Θ is non-singular. As an application, in the case of dimensions 2 and 3, we construct a new linear basis of the space of abelian functions which are singular only on Θ in terms of logarithmic derivatives of the higher-dimensional σ-function.

Original languageEnglish
Pages (from-to)145-171
Number of pages27
JournalInternational Journal of Mathematics
Volume19
Issue number2
DOIs
Publication statusPublished - Feb 1 2008

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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