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 intersection theory, we define the partial differential Chow form for an irreducible partial differential variety $V$ of Kolchin polynomial ${\omega }_V(t)=(d+1)\left(\genfrac{}{}{0ex}{}{t+m}{m}\right)-\left(\genfrac{}{}{0ex}{}{t+m-s}{m}\right)$. 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.

30 pages