Regularity and Normality of the Secant Variety to a Projective Curve

2006/10/02 by Peter Vermeire, Vermeire, Peter
Mathematics · #14D20 #14F05 #14J60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematics and Applications #math.AC #math.AG #msc:14D20 #msc:14F05 #msc:14J60

paper · pdf · doi:10.48550/arxiv.math/0610081

Version to appear in Journal of Algebra; evidence for main conjectures added

openalex publication_date 2006/10/02 · arxiv created 2007/10/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a smooth curve of genus g embedded by a line bundle of degree at least 2g+3 we show that the ideal sheaf of the secant variety is 5-regular. This bound is sharp with respect to both the degree of the embedding and the bound on the regularity. Further, we show that the secant variety is projectively normal for the generic embedding of degree at least 2g+3. We also give a conjectural description of the resolutions of the ideals of higher secant varieties.

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