TY - JOUR
T1 - Differential structure of Abelian functions
AU - Cho, Koji
AU - Nakayashiki, Atsushi
N1 - Funding Information:
This research is supported by Grant-in-Aid for Scientific Research (B) 17340048. The results of this paper were presented at the workshop “Integrable Systems, Geometry and Abelian Functions” held at Tokyo Metropolitan University, May 2005. We would like to thank Martin Guest, Yoshihiro Onishi and Shigeki Matsutani for organizing the stimulating workshop. We are also grateful to Victor Enolskii for answering questions and valuable comments.
PY - 2008/2
Y1 - 2008/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=44349166997&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=44349166997&partnerID=8YFLogxK
U2 - 10.1142/S0129167X08004595
DO - 10.1142/S0129167X08004595
M3 - Article
AN - SCOPUS:44349166997
VL - 19
SP - 145
EP - 171
JO - International Journal of Mathematics
JF - International Journal of Mathematics
SN - 0129-167X
IS - 2
ER -