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The Noether–Lefschetz Theorem Via Vanishing of Coherent Cohomology

Published online by Cambridge University Press:  20 November 2018

G. V. Ravindra
G. V. Ravindra*
Affiliation:
Department of Mathematics, Washington University, St. Louis, MO 63130, U.S.A. e-mail: ravindra@math.wustl.edu
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Abstract

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We prove that for a generic hypersurface in ${{\mathbb{P}}^{2n+1}}$ of degree at least $2\,+\,2/n$, the $n$-th Picard number is one. The proof is algebraic in nature and follows from certain coherent cohomology vanishing.

Keywords

14C1514C25Noether–Lefschetzalgebraic cyclesPicard number
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 2 , 01 June 2008 , pp. 283 - 290
Copyright
Copyright © Canadian Mathematical Society 2008

References

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