Abstract
Given a 0-dimensional scheme [Formula: see text] in the projective [Formula: see text]-space [Formula: see text] over a field [Formula: see text], we are interested in studying the Kähler different of [Formula: see text] and its applications. Using the Kähler different, we characterize the generic position and Cayley–Bacharach properties of [Formula: see text] in several certain cases. When [Formula: see text] is in generic position, we prove a generalized version of the Apéry–Gorenstein–Samuel theorem about arithmetically Gorenstein schemes. We also characterize 0-dimensional complete intersections in terms of the Kähler different and the Cayley–Bacharach property.
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