English

Square-free Groebner degenerations

Commutative Algebra 2020-03-12 v3 Algebraic Geometry Combinatorics

Abstract

Let I be a homogeneous ideal of a polynomial ring S. We prove that if the initial ideal J of I, w.r.t. a term order on S, is square-free, then the extremal Betti numbers of S/I and of S/J coincide. In particular, depth(S/I)=depth(S/J) and reg(S/I)=reg(S/J).

Keywords

Cite

@article{arxiv.1805.11923,
  title  = {Square-free Groebner degenerations},
  author = {Aldo Conca and Matteo Varbaro},
  journal= {arXiv preprint arXiv:1805.11923},
  year   = {2020}
}

Comments

Minor changes throughout. A compressed version of the paper will appear in Inventions Mathematicae

R2 v1 2026-06-23T02:13:10.846Z