Differential Structure of Abelian Functions
Algebraic Geometry
2007-05-23 v1 Quantum Algebra
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.
Cite
@article{arxiv.math/0604267,
title = {Differential Structure of Abelian Functions},
author = {K. Cho and A. Nakayashiki},
journal= {arXiv preprint arXiv:math/0604267},
year = {2007}
}
Comments
25 pages