2005/02/07 by Juan Migliore, Juan C. Migliore, Migliore, Juan C. · 1 citation
Mathematics · #13D40 #14C20 #14M05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematics and Applications #math.AC #math.AG #msc:13D40 #msc:14C20 #msc:14M05
paper · pdf · doi:10.48550/arxiv.math/0502145
27 pages; expository paper
arxiv created 2005/02/07 · openalex publication_date 2005/02/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compare and contrast results of E. Davis, of A. Bigatti, A.V. Geramita and the author, and of J. Ahn and the author. The underlying idea is that certain numerical conditions on the Hilbert function of a finite set of points in projective space force geometric consequences on the base loci of the linear systems of hypersurfaces containing the points. When the points have uniform position, this tends to force better behavior for these base loci. However, unexpected behavior is still possible, and we give examples.