Geometric Divisors in Normal Local Domains

John Brevik; Scott Nollet

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arXiv · 1606.01977

Geometric Divisors in Normal Local Domains

John Brevik·Scott Nollet

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Abstract

Let A be the local ring at a point of a normal complex variety with completion R. Srinivas has asked about the possible images of the induced map from Cl A to Cl R over all geometric normal domains A with fixed completion R. We use Noether-Lefschetz theory to prove that all finitely generated subgroups are possible in some familiar cases. As a byproduct we show that every finitely generated abelian group appears as the class group of the local ring at the vertex of a cone over some smooth complex variety of each positive dimension.

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John Brevik, Scott Nollet. 2016-06-06. Geometric Divisors in Normal Local Domains. https://arxiv.org/abs/1606.01977

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