The Kähler different of a 0-dimensional scheme

2022/04/21 by Long, Le Ngoc · 1 citation
#14M05 #14M10 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13C13 #Secondary 13D40

paper · doi:10.48550/arxiv.2204.10427

Abstract

Given a 0-dimensional scheme \mathbbX in the projective n-space ℙⁿ_K over a field K, we are interested in studying the Kähler different of \mathbbX and its applications. Using the Kähler different, we characterize the generic position and Cayley-Bacharach properties of \mathbbX in several certain cases. When \mathbbX 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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• The Cayley-Bacharach property and the Levinson-Ullery conjecture

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