On the Castelnuovo-Mumford regularity of subspace arrangements

Abstract

Let $X$ be the union of $n$ generic linear subspaces of codimension $>1$ in ${\mathbb{P}}^d$. Improving an earlier bound due to Derksen and Sidman, we prove that the Castelnuovo-Mumford regularity of $X$ satisfies $\mathrm{reg}(X)\le n-[n/(2d-1)]$.

Fixed typos, improved presentation. Accepted for publication at the Journal of the European Mathematical Society (June 2026)