English

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.

Keywords

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

R2 v1 2026-06-22T17:49:07.514Z