Reduction numbers and initial ideals
Commutative Algebra
2007-05-23 v1
Abstract
The reduction number r(A) of a standard graded algebra A is the least integer k such that there exists a minimal reduction J of the homogeneous maximal ideal m of A such that Jm^k=m^{k+1}. Vasconcelos conjectured that the reduction number of A=R/I can only increase by passing to the initial ideal, i.e r(R/I)\leq r(R/in(I)). The goal of this note is to prove the conjecture.
Keywords
Cite
@article{arxiv.math/0210064,
title = {Reduction numbers and initial ideals},
author = {Aldo Conca},
journal= {arXiv preprint arXiv:math/0210064},
year = {2007}
}
Comments
6 pages