On the Dedekind different of a Cayley-Bacharach scheme

2017/04/12 by Martin Kreuzer, Kreuzer, Martin, Tran N. K. Linh +3 · 1 citation
Mathematics · #13C13 #13D40 #14M05 #14N05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #msc:13C13 #msc:13D40 #msc:14M05 #msc:14N05

paper · pdf · doi:10.48550/arxiv.1704.03702

arxiv created 2017/04/12 · openalex publication_date 2017/04/12 · arxiv updated 2017/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a 0-dimensional scheme \mathbbX in a projective space ℙⁿ_K over a field K, we characterize the Cayley-Bacharach property of \mathbbX 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.

Cited by

• The Cayley-Bacharach property and the Levinson-Ullery conjecture

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