2010/09/01 by Xiao-Shan Gao, Gao, Xiao-Shan, Wěi Li +4 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #14C05 #14Q99 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Nonlinear Waves and Solitons #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.1009.0148
Although essentially the same, the new version contains many modifications
openalex publication_date 2010/09/01 · arxiv created 2011/07/30 · arxiv updated 2011/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 most of the properties of the Chow form in the algebraic case are established for its differential counterpart. Furthermore, the generalized differential Chow form is defined and its properties are proved. As an application of the generalized differential Chow form, the differential resultant of n+1 generic differential polynomials in n variables is defined and properties similar to that of the Macaulay resultant for multivariate polynomials are proved.