2002/09/15 by David Eisenbud, Eisenbud, David, Craig Huneke +3
Computer Science · Mathematics · #13C15 #13C40 #14M12 #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:13C15 #msc:13C40 #msc:14M12
paper · pdf · doi:10.48550/arxiv.math/0209184
21 pages, in AMS TeX
arxiv created 2002/09/15 · openalex publication_date 2002/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The classical "generalized principal ideal theorems" of Macaulay, Eagon-Northcott, and others give sharp bounds on the heights of determinantal ideals in arbitrary rings. But in regular local rings (or graded polynomial rings) these are far from sharp, and various questions about vector bundles, as well as other questions in commutative algebra, amount to asking what the real bounds are. We give partial answers, and more generally we prove new height bounds in local rings of given embedding codimension. Our theorems extend and sharpen results of Faltings and Bruns.