Transactions of the American Mathematical Society

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ISSN 1088-6850(e) ISSN 0002-9947(p)

Hypersurfaces cutting out a projective variety

Author(s): Atsushi Noma
Journal: Trans. Amer. Math. Soc. 362 (2010), 4481-4495.
MSC (2010): Primary 14N05, 14N15
Posted: April 6, 2010
MathSciNet review: 2645037
Retrieve article in: PDF

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Abstract: Let be a nondegenerate projective variety of degree and codimension 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 and a line in $\mathbb{P}^{N}$ at most if $L \not \subseteq X$ ? Is the scheme-theoretic intersection of all hypersurfaces of degree at most containing equal to ? To study the second problem, we look at the locus of points from which is projected nonbirationally.

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