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Differential Chow Form for Projective Differential Variety
In this paper, a generic intersection theorem in projective differential
algebraic geometry is presented. Precisely, the intersection of an irreducible
projective differential variety of dimension d>0 and order h with a generic
projective differential hyperplane is shown to be an irreducible projective
differential variety of dimension d-1 and order h. Based on the generic
intersection theorem, the Chow form for an irreducible projective differential
variety is defined and most of the properties of the differential Chow form in
affine differential case are established for its projective differential
counterpart. Finally, we apply the differential Chow form to a result of linear
dependence over projective varieties given by Kolchin.Comment: 17 page
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