Regularity jumps for powers of ideals

Details Regularity jumps for powers of ideals Regularity jumps for powers of ideals

2003-10-31

arxiv.org/abs/math/0310493v1

Mathematics

Commutative Algebra

Scientific paper

The Castelnuovo-Mumford regularity $\reg(I)$ is one of the most important invariants of a homogeneous ideal $I$ in a polynomial ring. A basic question is how the regularity behaves with respect to taking powers of ideals. It is known that in the long-run $\reg(I^k)$ is a linear function of $k$. We show that in the short-run the regularity of $I^k$ can be quite "irregular". For any given integer $d>1$ we construct an ideal $J$ generated by $d+5$ monomials of degree $d+1$ in 4 variables such that $\reg(J^k)=k(d+1)$ for every $k

Affiliated with

Also associated with

No associations

Rating

Regularity jumps for powers of ideals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Regularity jumps for powers of ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regularity jumps for powers of ideals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-635389