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Grothendieck–Lefschetz theorem with base locus

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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 C of dimension ≥ 4 are completions of UFDs of finite type over C.

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Authors and Affiliations

  1. Department of Mathematics and Statistics California State, University at Long Beach, Long Beach, CA, 90840, USA

    John Brevik

  2. Department of Mathematics, Texas Christian University, Fort Worth, TX, 76129, USA

    Scott Nollet

Authors
  1. John Brevik
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  2. Scott Nollet
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Correspondence to John Brevik.

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Brevik, J., Nollet, S. Grothendieck–Lefschetz theorem with base locus. Isr. J. Math. 212, 107–122 (2016). https://doi.org/10.1007/s11856-016-1281-1

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  • DOI: https://doi.org/10.1007/s11856-016-1281-1

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