Geodesic
The Noether–Lefschetz Theorem Via Vanishing of Coherent Cohomology
Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 283-290

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DOI

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.
DOI : 10.4153/CMB-2008-028-x
Mots-clés : 14C15, 14C25, Noether–Lefschetz, algebraic cycles, Picard number 
Ravindra, G. V. The Noether–Lefschetz Theorem Via Vanishing of Coherent Cohomology. Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 283-290. doi: 10.4153/CMB-2008-028-x
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     author = {Ravindra, G. V.},
     title = {The {Noether{\textendash}Lefschetz} {Theorem} {Via} {Vanishing} of {Coherent} {Cohomology}},
     journal = {Canadian mathematical bulletin},
     pages = {283--290},
     year = {2008},
     volume = {51},
     number = {2},
     doi = {10.4153/CMB-2008-028-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-028-x/}
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