  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.
