Hypersurfaces cutting out a projective variety
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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.References
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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
- MR Author ID: 315999
- Email: noma@edhs.ynu.ac.jp
- 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.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 4481-4495
- MSC (2010): Primary 14N05, 14N15
- DOI: https://doi.org/10.1090/S0002-9947-10-05054-3
- MathSciNet review: 2645037