2002/10/03 by Jon Eivind Vatne, Vatne, Jon Eivind · 1 citation
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/0210042
46 pages; based on parts of author's thesis
arxiv created 2002/10/03 · openalex publication_date 2002/10/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a systematic approach to constructing non-reduced, locally Cohen-Macaulay schemes with reduced support a smooth projective variety. The hierarchy of such structures includes a lot of information about the underlying variety, its embeddings in projective space and the behaviour of its vector bundles. For instance, Hartshorne's conjecture on complete intersections in codimension two is reformulated in terms of existence of certain schemes of degrees two and three. There are many examples, and classifications of multiple structures with special properties (like low degree).