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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On quasi-complete intersections of codimension $ 2$


Author: Youngook Choi
Journal: Proc. Amer. Math. Soc. 134 (2006), 1249-1256
MSC (2000): Primary 14M07, 14N05, 14M06
Published electronically: December 14, 2005
MathSciNet review: 2199166
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Abstract: In this paper, we prove that if $ X\subset\mathbb{P}^n$, $ n\ge 4$, is a locally complete intersection of pure codimension $ 2$ and defined scheme-theoretically by three hypersurfaces of degrees $ d_1\ge d_2\ge d_3$, then $ H^1(\mathbb{P}^n,\mathcal{I}_X(j))=0$ for $ j<d_3$ using liaison theory and the Arapura vanishing theorem for singular varieties. As a corollary, a smooth threefold $ X\subset\mathbb{P}^5$ is projectively normal if $ X$ is defined by three quintic hypersurfaces.


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Additional Information

Youngook Choi
Affiliation: Department of Mathematics, Korea Advanced Institute of Science and Technology, 373-1 Gusung-dong Yusung-gu, Daejeon, Korea
Email: ychoi@math.kaist.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08425-X
PII: S 0002-9939(05)08425-X
Keywords: Quasi-complete intersections, liaison, normality, defining equations
Received by editor(s): September 10, 2004
Published electronically: December 14, 2005
Additional Notes: The author was supported in part by KRF (grant No. KRF-2002-070-C00003)
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.