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- W1963571013 abstract "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 ai(X)=dimk[ToriR(A,k)]i+1. Green's Strong Castelnuovo Lemma (SCL) shows that if the points are in general position, then an−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: an−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." @default.
- W1963571013 created "2016-06-24" @default.
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- W1963571013 date "2010-02-01" @default.
- W1963571013 modified "2023-09-26" @default.
- W1963571013 title "A generalization of the Strong Castelnuovo Lemma" @default.
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- W1963571013 doi "https://doi.org/10.1016/j.jalgebra.2009.11.038" @default.
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