The Dedekind different of a Cayley–Bacharach scheme

Abstract

Given a 0-dimensional scheme [Formula: see text] in a projective space [Formula: see text] over a field [Formula: see text], we characterize the Cayley–Bacharach property (CBP) of [Formula: see text] in terms of the algebraic structure of the Dedekind different of its homogeneous coordinate ring. Moreover, we characterize Cayley–Bacharach schemes by Dedekind’s formula for the conductor and the complementary module, we study schemes with minimal Dedekind different using the trace of the complementary module, and we prove various results about almost Gorenstein and nearly Gorenstein schemes.