Local Picard Groups

John Brevik; Scott Nollet

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arXiv · 1110.1867

Local Picard Groups

John Brevik·Scott Nollet

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Abstract

We use our extension of the Noether-Lefschetz theorem to describe generators of the class groups at the local rings of singularities of very general hypersurfaces containing a fixed base locus. We give several applications, including (1) every subgroup of the class group of the completed local ring of a rational double point arises as the class group of such a singularity on a surface in complex projective 3-space and (2) every complete local ring arising from a normal hypersurface singularity over the complex numbers is the completion of a unique factorization domain of essentially finite type over the complex numbers.

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BibTeX RIS

John Brevik, Scott Nollet. 2011-10-09. Local Picard Groups. https://arxiv.org/abs/1110.1867

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