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KOSZUL PROPERTY FOR POINTS IN PROJECTIVE SPACES

ALDO CONCA, NGÔ VIÊT TRUNG and GIUSEPPE VALLA
Mathematica Scandinavica
Vol. 89, No. 2 (2001), pp. 201-216
Published by: Mathematica Scandinavica
Stable URL: http://www.jstor.org/stable/24491957
Page Count: 16
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KOSZUL PROPERTY FOR POINTS IN PROJECTIVE SPACES
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Abstract

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 Pn. 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 s ≤ 1 + n + n2/4. If s ≤ 2n and the points are in linear general position, then we show that there exists a system of coordinates x0,..., xn of Pn such that all the ideals (x0, x1,..., xi) with 0 ≤ i ≤ n have a linear R-free resolution.

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