Partial differential Chow forms and a type of partial differential Chow varieties

摘要

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 xotTHORN 1/4 od thorn 1THORN t thorn m m t thorn m s m :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.