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

Abstract

We first present an intersection theory of partial differential varieties with quasi-generic differential hypersurfaces. Then, based on the generic differential intersection theory, we define the partial differential Chow form for an irreducible partial differential variety V of Kolchin polynomial ω V (t) = (d + 1) t+m m − t+m−s m . And we establish for the partial differential Chow form most of the basic properties of the ordinary differential Chow form. Furthermore, we prove the existence of a type of partial differential Chow varieties.