2011/07/16 by Wei Li, Xiao-Shan Gao, Li, Wei +1
Computer Science · Mathematics · #14C05 #14Q99 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Primary 12H05 #Secondary 14C17 #Symbolic Computation (cs.SC) #cs.SC #math.AG #msc:12H05 #msc:14C05 #msc:14C17 #msc:14Q99
paper · pdf · doi:10.48550/arxiv.1107.3205
17 pages
arxiv created 2011/07/16 · openalex publication_date 2011/07/16 · arxiv updated 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.