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Multisecant subspaces to smooth projective varieties in arbitrary characteristic

Author: Atsushi Noma
Journal: Proc. Amer. Math. Soc. 137 (2009), 3985-3990
MSC (2000): Primary 14N05, 14H45
Published electronically: July 1, 2009
MathSciNet review: 2538558
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Abstract: Let $ X \subseteq \mathbb{P}^{N}$ be a projective variety of dimension $ n\geq 1$, degree $ d$, and codimension $ e$, not contained in any hyperplane, defined over an algebraically closed field $ \Bbbk$ of arbitrary characteristic. We show that if a $ k$-dimensional linear subspace $ M$ meets $ X$ at the smooth locus such that $ X\cap M$ is finite and locally lies on a smooth curve, then the length $ l(X\cap M)$ does not exceed $ d-e+k-\min \{g,e-k\}$ for the sectional genus $ g$ of $ X$.

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Additional Information

Atsushi Noma
Affiliation: Department of Mathematics, Faculty of Education and Human Sciences, Yokohama National University, Yokohama 240-8501, Japan

Keywords: Secant line, secant space, sectional genus
Received by editor(s): June 1, 2007
Received by editor(s) in revised form: March 20, 2009
Published electronically: July 1, 2009
Additional Notes: This work was partially supported by the Japan Society for the Promotion of Science.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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