2013/06/18 by Mike Janssen, Janssen, Mike
Computer Science · Mathematics · #14 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14
paper · pdf · doi:10.48550/arxiv.1306.4387
9 pages; updated version with a simpler proof of Proposition 2.10 and updated references
openalex publication_date 2013/06/18 · arxiv created 2013/06/29 · arxiv updated 2013/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We follow the lead of Bocci and Chiantini and show how differences in the invariant alpha can be used to classify certain classes of subschemes of P3. Specifically, we will seek to classify arithmetically Cohen-Macaulay codimension 2 subschemes of P3 in the manner Bocci and Chiantini classified points in P2. The first section will seek to motivate our consideration of the invariant alpha by relating it to the Hilbert function and gamma, following the work of Bocci and Chiantini, and Dumnicki, et. al. The second section will contain our results classifying arithmetically Cohen-Macaulay codimension 2 subschemes of P3. This work is adapted from the author's Ph.D. dissertation.