Algorithms for Checking Zero-Dimensional Complete Intersections
Abstract
Given a 0-dimensional affine K-algebra R=K[x_1,...,x_n]/I, where I is an ideal in a polynomial ring K[x_1,...,x_n] over a field K, or, equivalently, given a 0-dimensional affine scheme, we construct effective algorithms for checking whether R is a complete intersection at a maximal ideal, whether R is locally a complete intersection, and whether R is a strict complete intersection. These algorithms are based on Wiebe's characterisation of 0-dimensional local complete intersections via the 0-th Fitting ideal of the maximal ideal. They allow us to detect which generators of I form a regular sequence resp. a strict regular sequence, and they work over an arbitrary base field K. Using degree filtered border bases, we can detect strict complete intersections in certain families of 0-dimensional ideals.
Cite
@article{arxiv.1903.09563,
title = {Algorithms for Checking Zero-Dimensional Complete Intersections},
author = {Martin Kreuzer and Le Ngoc Long and Lorenzo Robbiano},
journal= {arXiv preprint arXiv:1903.09563},
year = {2019}
}
Comments
Small changes. To be published in Journal of Commutative Algebra