Regularity and Normality of the Secant Variety to a Projective Curve

Details Regularity and Normality of the Secant Variety to a Projective Curve Regularity and Normality of the Secant Variety to a Projective Curve

2006-10-02

arxiv.org/abs/math/0610081v3

Mathematics

Algebraic Geometry

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

Scientific paper

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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