A sublinear bound for the regularity of subspace arrangements

Xin Hong; Yi-Song Huang; Manolis Tsakiris

A sublinear bound for the regularity of subspace arrangements

Commutative Algebra 2026-07-21 v1 Algebraic Geometry

Authors: Xin Hong , Yi-Song Huang , Manolis Tsakiris

Abstract

Let $X$ be the union of $k$ generic linear spaces in $\PP^n$ of codimension at least $2$ . We prove that the Castelnuovo-Mumford regularity of the vanishing ideal of $X$ grows in order not more than $\sqrt{k}$ , and that this is an order-tight bound when the codimension equals $2$ .

Keywords

Castelnuovo-Mumford regularity subspace arrangements vanishing ideal generic linear spaces projective space

Cite

@article{arxiv.2607.18892,
  title  = {A sublinear bound for the regularity of subspace arrangements},
  author = {Xin Hong and Yi-Song Huang and Manolis Tsakiris},
  journal= {arXiv preprint arXiv:2607.18892},
  year   = {2026}
}