Linkage on arithmetically Cohen-Macaulay schemes with application to the classification of curves of maximal genus

2002/11/20 by Rita Ferraro, Ferraro, Rita
Mathematics · #13C10 #13C14 #13C40 #14M06 #14Q05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13C10 #msc:13C14 #msc:13C40 #msc:14M06 #msc:14Q05

paper · pdf · doi:10.48550/arxiv.math/0211331

Latex, 22 pages. Submitted to "Journal in Pure and Applied Algebra". It is a revised and improved version of math.AG/0105094

arxiv created 2002/11/20 · arxiv updated 2009/11/30

Abstract

In this paper the author provides a generalization of classical linkage, i.e. linkage by a complete intersection of dim. 0 or 1 on arithmetically Cohen-Macaulay schemes of any dimension. Namely she looks at residuals in the scheme theoretic intersection of an aCM scheme of dim. r (resp. r+1) with r hypersurfaces of degree a₁,...,a_r. When the aCM scheme is singular a complete intersection on it may not be Gorenstein, in this case classical linkage, even if suitably generalized, does not apply. The main purpose of this paper is to prove some results related to the invariance of the deficiency module under such linkage. 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.

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