Arithmetic properties of the first secant variety to a projective variety

Details Arithmetic properties of the first secant variety to a projective variety Arithmetic properties of the first secant variety to a projective variety

2010-10-12

arxiv.org/abs/1010.2386v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

Under an explicit positivity condition, we show the first secant variety of a linearly normal smooth variety is projectively normal, give results on the regularity of the ideal of the secant variety, and give conditions on the variety that are equivalent to the secant variety being arithmetically Cohen-Macaulay. Under this same condition, we then show that if $X$ satisfies $N_{p+2\dim(X)}$, then the secant variety satisfies $N_{3,p}$.

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