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1. CMB 2008 (vol 51 pp. 283)
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The Noether--Lefschetz Theorem Via Vanishing of Coherent Cohomology 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 Categories:14C15, 14C25 |