Arithmetically Cohen-Macaulay Curves cut out by Quadrics

1992/02/19 by Sheldon Katz, Katz, Sheldon · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9202018

6 pages, LaTeX Version 2.09

openalex publication_date 1992/02/19 · arxiv created 1992/03/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Addressing a question of M. Stillman, it had been shown by Ein, Eisenbud, and the author that in a projective space of dimension at most 5, every arithmetically Cohen-Macaulay curve which is cut out by quadrics scheme- theoretically also has its homogeneous ideal generated by quadrics. In this note it is shown that this is not the case in higher dimensional spaces.

Citations

• On the projective normality of complete linear series on an algebraic curve

Cited by

• Analysis on some infinite modules, inner projection, and applications

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