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Noether–Lefschetz theory with base locus

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Abstract

Let \(Z\) be a closed subscheme of a smooth complex projective variety \(Y\subseteq \mathbb {P}^N\), with \(\dim \,Y=2r+1\ge 3\). We describe the intermediate Néron–Severi group (i.e. the image of the cycle map \(A_r(X)\rightarrow H_{2r}(X;\mathbb {Z})\)) of a general smooth hypersurface \(X\subset Y\) of sufficiently large degree containing \(Z\).

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Acknowledgments

We would like to thank Ciro Ciliberto and Claudio Murolo for valuable discussions and suggestions on the subject of this paper.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 , Roma, Italy

    Vincenzo Di Gennaro

  2. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, P.le Tecchio 80, 80125 , Napoli, Italy

    Davide Franco

Authors
  1. Vincenzo Di Gennaro
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  2. Davide Franco
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Correspondence to Vincenzo Di Gennaro.

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Di Gennaro, V., Franco, D. Noether–Lefschetz theory with base locus. Rend. Circ. Mat. Palermo 63, 257–276 (2014). https://doi.org/10.1007/s12215-014-0156-8

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  • DOI: https://doi.org/10.1007/s12215-014-0156-8

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