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# The Noether--Lefschetz Theorem Via Vanishing of Coherent Cohomology

Published:2008-06-01
Printed: Jun 2008
• G. V. Ravindra
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## Abstract

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: Noether--Lefschetz, algebraic cycles, Picard number
 MSC Classifications: 14C15 - (Equivariant) Chow groups and rings; motives 14C25 - Algebraic cycles