Syzygy bundles and the weak Lefschetz property of almost complete intersections
Commutative Algebra
2016-06-07 v1
Abstract
Deciding the presence of the weak Lefschetz property often is a challenging problem. In this work an in-depth study is carried out in the case of Artinian monomial ideals with four generators in three variables. We use a connection to lozenge tilings to describe semistability of the syzygy bundle of such an ideal, to determine its generic splitting type, and to decide the presence of the weak Lefschetz property. We provide results in both characteristic zero and positive characteristic.
Keywords
Cite
@article{arxiv.1606.01809,
title = {Syzygy bundles and the weak Lefschetz property of almost complete intersections},
author = {David Cook and Uwe Nagel},
journal= {arXiv preprint arXiv:1606.01809},
year = {2016}
}
Comments
22 pages. arXiv admin note: substantial text overlap with arXiv:1305.1314