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We show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties.
I. Satake
1956
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M. Saito
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V. V. Batyrev
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V. V. Batyrev and D. A. Cox
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D. Maulik, R. Pandharipande, and A. Pixton
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arXiv:hep-th/0409290v1
F. Rohsiepe
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D. A. Cox and S. Katz
1999
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J. Carlson, S. Müller-Stach, and C. Peters
2003
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Classical setting: line bundles and linear series
R. Lazarsfeld · 2004
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G. V. Ravindra and V. Srinivas
2006
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R. Kloosterman
2007
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Z. Z. Wang and D. Zaffran
2009
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A. Klemm, D. Maulik, R. Pandharipande, and E. Scheidegger
2010
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