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arXiv · 0806.1243

Noether-Lefschetz theorem with base locus

John Brevik·Scott Nollet
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Abstract

We compute the class groups of very general normal surfaces in complex projective three-space containing an arbitrary base locus $Z$, thereby extending the classic Noether-Lefschetz theorem (the case when $Z$ is empty). Our method is an adaptation of Griffiths and Harris' degeneration proof, simplified by a cohomology and base change argument. We give applications to computing Picard groups, which generalize several known results.

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John Brevik, Scott Nollet. 2009-11-03. Noether-Lefschetz theorem with base locus. https://doi.org/10.1093/imrn%2Frnq106

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