Monomial generators of complete planar ideals
Algebraic Geometry
2017-10-31 v3 Commutative Algebra
Abstract
We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the minimal log-resolution of the ideal. Furthermore, the monomial expression given by our method is an equisingularity invariant of the ideal. As an outcome, we provide a geometric method to compute the integral closure of a planar ideal and we apply our algorithm to some families of complete ideals.
Cite
@article{arxiv.1701.03503,
title = {Monomial generators of complete planar ideals},
author = {Maria Alberich-Carramiñana and Josep Alvarez Montaner and Guillem Blanco},
journal= {arXiv preprint arXiv:1701.03503},
year = {2017}
}
Comments
22 pages. Title change and major revision of the previous version. Applications to families of complete ideals included