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).
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