The Kähler different of a 0-dimensional scheme

Abstract

Given a 0-dimensional scheme X in the projective n-space P n K over a field K, we are interested in studying the Kähler different of X and its applications. Using the Kähler different, we characterize the generic position and Cayley-Bacharach properties of X in several certain cases. When X 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.