Peter Vermeire
Published 2006-10-02, updated 2007-10-23Version 3
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.
Comments: Version to appear in Journal of Algebra; evidence for main conjectures added
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