Positivity and complexity of ideal sheaves

Details Positivity and complexity of ideal sheaves Positivity and complexity of ideal sheaves

2000-07-05

arxiv.org/abs/math/0007023v1

Mathematics

Algebraic Geometry

Scientific paper

The problem of bounding the "complexity" of a polynomial ideal in terms of the degrees of its generators has attracted considerable interest, brought into focus by the influential survey of Bayer and Mumford. The present paper examines some of these results and questions from a geometric perspective. Specifically, motivated by work of Paoletti we introduce an invariant s(I) that measures the "positivity" of an ideal sheaf I. Degree bounds on generators of I yield bounds on this s-invariant, but s(I) may be small even when the degrees of its generators are large. We prove that s(I) computes the asymptotic Castelnuovo-Mumford regularity of large powers of I, and bounds the asymptotic behavior of several other measures of complexity. We also show that this s-invariant behaves very well with respect to natural geometric and algebraic operations, which leads to considerably simplified constructions of varieties with irrational asymptotic regularity. The main tools are intersection theory and vanishing theorems.

Affiliated with

Also associated with

No associations

Rating

Positivity and complexity of ideal sheaves 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 Positivity and complexity of ideal sheaves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positivity and complexity of ideal sheaves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-171762