2004/05/19 by David Eisenbud, Eisenbud, David, Craig Huneke +3 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.math/0405373
arxiv created 2004/05/19 · arxiv updated 2009/12/01
Let S=K[x1,..., xn], let A,B be finitely generated graded S-modules, and let m=(x1,...,xn). We give bounds for the Castelnuovo-Mumford regularity of the local cohomology of Tori(A,B) under the assumption that the Krull dimension of Tor1(A,B) is at most 1. We apply the results to syzygies, Groebner bases, products and powers of ideals, and to the relationship of the Rees and Symmetric algebras. For example we show that any homogeneous linearly presented m-primary ideal has some power equal to a power of m; and if the first (roughly) (n-1)/2 steps of the resolution of I are linear, then I2 is a power of m.