Koszul property for points in projective spaces - Conca, Aldo; Trung, Ngô Viêt; Valla, Giuseppe (MATHEMATICA SCANDINAVICA, 2001)
A graded K-algebra R is said to be Koszul if the minimal R-free graded resolution of K is linear. In this paper we study the Koszul property of the homogeneous coordinate ring R of a set of s points in the complex projective space P^n. Kempf proved that R is Koszul if s≤ 2n and the points are in general linear position. If the coordinates of the points are algebraically independent over Q, then we prove that R is Koszul if and only if s1 +n + n^2/4. If s2n and the points are in linear general position, then we show that there exists a system of coordinates x_0,…,x_n of P^n such that all the ideals (x_0,x_1,…,x_i) with 0i n have a linear R-free resolution.