2009/05/29 by Seyed Hamid Hassanzadeh, Hassanzadeh, Seyed Hamid
Computer Science · Mathematics · #13D25 #13D45 #13H10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.0905.4901
openalex publication_date 2009/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we study the structure of residual intersections via\nconstructing a finite complex which is acyclic under some sliding depth\nconditions on the cycles of the Koszul complex. This complex provides\ninformation on an ideal which coincides with the residual intersection in the\ncase of geometric residual intersection; and is closely related to it in\ngeneral. A new success obtained through studying such a complex is to prove the\nCohen-Macaulayness of residual intersections of a wide class of ideals. For\nexample we show that, in a Cohen-Macaulay local ring, any geometric residual\nintersection of an ideal that satisfies the sliding depth condition is\nCohen-Macaulay; this is an affirmative answer to one of the main open questions\nin the theory of residual intersection. The complex we construct also provides\na bound for the Castelnuovo-Mumford regularity of a residual intersection in\nterm of the degrees of the minimal generators.\n