Commuting differential operators and higher-dimensional algebraic varieties
Algebraic Geometry
2018-01-31 v4 Mathematical Physics
math.MP
Abstract
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of partial differential operators, and we investigate the properties of these geometric data. This construction is similar to the construction of a formal module of Baker-Akhieser functions. On the other hand, there is a recent generalization of Sato's theory which belongs to the third author of this paper. We compare both approaches to the commutative rings of partial differential operators in two variables.
Cite
@article{arxiv.1211.0976,
title = {Commuting differential operators and higher-dimensional algebraic varieties},
author = {Herbert Kurke and Denis Osipov and Alexander Zheglov},
journal= {arXiv preprint arXiv:1211.0976},
year = {2018}
}
Comments
25 p V2: minor change V3: revised version, to appear in Selecta Math V4: an inaccuracy in Th.2.1 is fixed