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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)



Hypersurfaces cutting out a projective variety

Author: Atsushi Noma
Journal: Trans. Amer. Math. Soc. 362 (2010), 4481-4495
MSC (2010): Primary 14N05, 14N15
Published electronically: April 6, 2010
MathSciNet review: 2645037
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Abstract: Let $ X$ be a nondegenerate projective variety of degree $ d$ and codimension $ e$ in a projective space $ \mathbb{P}^{N}$ defined over an algebraically closed field. We study the following two problems: Is the length of the intersection of $ X$ and a line $ L$ in $ \mathbb{P}^{N}$ at most $ d-e+1$ if $ L \not \subseteq X$? Is the scheme-theoretic intersection of all hypersurfaces of degree at most $ d-e+1$ containing $ X$ equal to $ X$? To study the second problem, we look at the locus of points from which $ X$ is projected nonbirationally.

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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, projection, hypersurface, defining equation
Received by editor(s): October 15, 2007
Published electronically: April 6, 2010
Additional Notes: This work was partially supported by Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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