2001/05/11 by Rita Ferraro, Ferraro, Rita · 1 citation
Mathematics · #13C10 #13C14 #13C40 #14M06 #14Q05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric and Algebraic Topology #math.AC #math.AG #msc:13C10 #msc:13C14 #msc:13C40 #msc:14M06 #msc:14Q05
paper · pdf · doi:10.48550/arxiv.math/0105094
Latex 25 pages. To be submitted to "Journal in Pure and Applied Algebra"
arxiv created 2001/05/11 · openalex publication_date 2001/05/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper the author provides a generalization of classical linkage, i.e. linkage by a complete intersection, in a different context. Namely she looks at residuals in the scheme theoretic intersection of a rational normal surface or 3-fold with two hypersurfaces of degree a and b. When the scroll is singular a complete intersection of type (a, b) on it may not be Gorenstein, in this case classical linkage, even if suitably generalized, does not apply. The main purpose of this article is to establish a framework allowing one to find relations between the dimension of some important cohomology groups attached to the two linked schemes. In the last part of the paper the author shows how to apply these results and techniques to the classification of curves C in Pn of degree d and maximal genus G(d, n, s) among those not contained in surfaces of degree less than a certain fixed one s.