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arXiv · 1601.05846

Grothendieck-Lefschetz Theorem with Base Locus

John Brevik·Scott Nollet
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Abstract

We compute the divisor class group of the general hypersurface Y of a complex projective normal variety X of dimension at least four containing a fixed base locus Z. We deduce that completions of normal local complete intersection domains of finite type over the complex numbers of dimension $\ge 4$ are completions of UFDs of finite type over the complex numbers.

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John Brevik, Scott Nollet. 2016-01-22. Grothendieck-Lefschetz Theorem with Base Locus. https://arxiv.org/abs/1601.05846

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