Koszul configurations of points in projective spaces

We prove a new criterion for the homogeneous coordinate ring of a finite set of points in Pn to be Koszul. Like the well-known criterion due to Kempf [G. Kempf, Syzygies for points in projective space, J. Algebra 145 (1992) 219–223] it involves only incidence conditions on linear spans of subsets of a given set. We also give a sufficient condition for the Koszul property to be preserved when passing to a subset of a finite set of points in Pn.