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Medientyp:
E-Artikel
Titel:
KOSZUL PROPERTY FOR POINTS IN PROJECTIVE SPACES
Beteiligte:
CONCA, ALDO;
TRUNG, NGÔ VIÊT;
VALLA, GIUSEPPE
Erschienen:
DANSK MATEMATISK FORENING / ÍSLENZKA STÆŘKFRAÆ̌KAFÉLAGǏK / NORSK MATEMATISK FORENING, 2001
Erschienen in:Mathematica Scandinavica
Sprache:
Englisch
ISSN:
0025-5521;
1903-1807
Entstehung:
Anmerkungen:
Beschreibung:
<p>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.</p>