Noether-lefschetz Theorem with Base Locus
نویسندگان
چکیده
For an arbitrary curve Z ⊂ P (possibly reducible, non-reduced, unmixed) lying on a normal surface, the general surface S of high degree containing Z is also normal, but often singular. We compute the class groups of the very general such surface, thereby extending the Noether-Lefschetz theorem (the special 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. Dedicated to Robin Hartshorne on his 70th birthday
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تاریخ انتشار 2009