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On the picard group of certain smooth surfaces in weighted projective spaces

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Algebraic Geometry

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 961))

Abstract

We consider a general member of a Lefschetz pencil of surfaces in weighted projective 3-spaces of type (1,1,a,b) where gad(a,b)=1. We show that such a surface either has Picard number equal to 1 or all of its 2-cohomolgy is algebraic.

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Author information

Authors and Affiliations

  1. Mathematisch Instituut der, Rijksuniversiteit Leiden, Wassenaarseweg 80, 2333 AL, Leiden, The Netherlands

    Joseph Steenbrink

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  1. Joseph Steenbrink
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Editor information

José Manuel Aroca Ragnar Buchweitz Marc Giusti Michel Merle

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© 1982 Springer-Verlag

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Steenbrink, J. (1982). On the picard group of certain smooth surfaces in weighted projective spaces. In: Aroca, J.M., Buchweitz, R., Giusti, M., Merle, M. (eds) Algebraic Geometry. Lecture Notes in Mathematics, vol 961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071290

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  • DOI: https://doi.org/10.1007/BFb0071290

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11969-2

  • Online ISBN: 978-3-540-39367-2

  • eBook Packages: Springer Book Archive

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