A generalization of the Strong Castelnuovo Lemma

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• 作者：Laura Ghezzi
• 关键词：Resolutions of points ; Linear syzygies ; Strong Castelnuovo Lemma
• 刊名：Journal of Algebra
• 出版年：2010
• 出版时间：15 February 2010
• 年：2010
• 卷：323
• 期：4
• 页码：1018-1035
• 全文大小：280 K

文摘

We consider a set X of distinct points in the n-dimensional projective space over an algebraically closed field k. Let A denote the coordinate ring of X, and let . Green's Strong Castelnuovo Lemma (SCL) shows that if the points are in general position, then a_n−1(X)≠0 if and only if the points are on a rational normal curve. Cavaliere, Rossi and Valla (1995) conjectured in [2] that if the points are not necessarily in general position the possible extension of the SCL should be the following: a_n−1(X)≠0 if and only if either the points are on a rational normal curve or in the union of two linear subspaces whose dimensions add up to n. In this work we prove the conjecture.