A generalization of the Strong Castelnuovo Lemma

作者：Ghezzi Laura^*

来源：Journal of Algebra, 2010, 323(4): 1018-1035.

DOI：10.1016/j.jalgebra.2009.11.038

• Resolutions of points
• Linear syzygies
• Strong Castelnuovo Lemma

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 a(i)(X) = dim(k)[Tor(i)(R)(A,k)](i+1). Green's Strong Castelnuovo Lemma (SCL) shows that if the points are in general position, then a(n-1)(X) not equal 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) not equal 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.

• 出版日期2010-2-15