2002/09/30 by Laurent Busé, Laurent Buse, Buse, Laurent
Computer Science · Mathematics · #13D02 (Secondary) #14M12 #14Q20 (Primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:13D02 #msc:14M12 #msc:14Q20
paper · pdf · doi:10.48550/arxiv.math/0209404
26 pages, 1 figure. LaTeX2e using amsart documentclass
arxiv created 2002/09/30 · openalex publication_date 2002/09/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct generalization of the resultant of a very ample vector bundle, it corresponds to a necessary and sufficient condition so that a given morphism between two vector bundles on a projective variety X has rank lower or equal to a given integer in at least one point. First some conditions are given for the existence of such a resultant and it is showed how to compute explicitly its degree. Then a result of A. Lascoux is used to obtain it as a determinant of a certain complex. Finally some more detailed results in the particular case where X is a projective space are exposed.