Abstract
We first present an intersection theory of irreducible partial differential varieties with quasi-generic differential hypersurfaces. Then, we define partial differential Chow forms for irreducible partial differential varieties whose Kolchin polynomials are of the form And we establish for partial differential Chow forms most of the basic properties of their ordinary differential counterparts. Furthermore, we prove that a certain type of partial differential Chow varieties exist.
Communicated by Jason Bell
2010 Mathematics Subject Classification:
Acknowledgements
The author is grateful to the anonymous referee for the helpful comments and constructive suggestions on a previous version of this manuscript.
Notes
1 By saying η free from we mean that
is a set of Δ-
-indeterminates.
2 Here, the orderly ranking is assumed to guarantee that the order of is bounded by t and thus obtain
when following the proof of Theorem 3.2 to prove the corollary.