1995/04/15 by Scott Nollet, Nollet, Scott
Mathematics · #13C40 #14M12 #14MO6 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #alg-geom #math.AC #math.AG #msc:13C40 #msc:14M12 #msc:14MO6
paper · pdf · doi:10.48550/arxiv.alg-geom/9504008
26 pages, amstex
arxiv created 1995/04/15 · openalex publication_date 1995/04/15 · arxiv updated 2015/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the problem of describing the integral subschemes within a fixed even linkage class Ł of subschemes in \Pn of codimension two. In the case that Ł is not the class of arithmetically Cohen-Macaulay subschemes, we associate to any X ∈ Ł two invariants θX and ηX. When taken with the height hX, each of these invariants determines the location of X in Ł, thought of as a poset under domination. In terms of these invariants, necessary conditions are given for integral subschemes. The necessary conditions are almost sufficient in the sense that if a subscheme X satisfies the necessary conditions and dominates an integral subscheme Y, then X can be deformed with constant cohomology through subschemes in Ł to an integral subscheme. In particular, if an even linkage class has a minimal element which is integral, then the conditions are both necessary and sufficient.