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Original Articles

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

Pages 3342-3371 | Received 15 Jan 2019, Accepted 26 Feb 2020, Published online: 19 Mar 2020
 

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 ω(t)=(d+1)(t+mm)(t+msm). 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 FU, we mean that U is a set of Δ-Fη-indeterminates.

2 Here, the orderly ranking is assumed to guarantee that the order of hl is bounded by t and thus obtain H(Y)0, when following the proof of Theorem 3.2 to prove the corollary.

Additional information

Funding

This work was supported by NSFC under Grants (11971029, 11688101, 11671014, and 11301519).

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