On the Castelnuovo–Mumford regularity of subspace arrangements

Abstract

Let $X$ be a union of $n$ generic linear subspaces of codimension $>1$ in ${\mathbb{P}}^d$. Improving an earlier bound due to Derksen and Sidman (2002), we prove that the Castelnuovo–Mumford regularity of $X$ satisfies $\mathrm{reg}(X)\le n-\lfloor n/(2d-1)\rfloor$.