Intersection theory in differential algebraic geometry: Generic intersections and the differential Chow form

@article{Gao2010IntersectionTI,
  title={Intersection theory in differential algebraic geometry: Generic intersections and the differential Chow form},
  author={X. Gao and Wei Li and Chunming Yuan},
  journal={arXiv: Algebraic Geometry},
  year={2010}
}
In this paper, an intersection theory for generic differential polynomials is presented. The intersection of an irreducible differential variety of dimension $d$ and order $h$ with a generic differential hypersurface of order $s$ is shown to be an irreducible variety of dimension $d-1$ and order $h+s$. As a consequence, the dimension conjecture for generic differential polynomials is proved. Based on the intersection theory, the Chow form for an irreducible differential variety is defined and… 
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