An application of Liaison theory to zero-dimensional schemes
Abstract
Given a 0-dimensional scheme X in a n-dimensional projective space PnK over an arbitrary field K, we use Liaison theory to characterize the Cayley-Bacharach property of X. Our result extends the result for sets of K-rational points given in [7]. In addition, we examine and bound the Hilbert function and regularity index of the Dedekind different of X when X has the Cayley-Bacharach property.
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