Noether-Lefschetz theorem with base locus

Details Noether-Lefschetz theorem with base locus Noether-Lefschetz theorem with base locus

2008-06-06

arxiv.org/abs/0806.1243v3

Mathematics

Algebraic Geometry

18 pages, amsart

Scientific paper

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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