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A conjecture of Beauville and Catanese revisited

Pink, Richard ; Roessler, Damian

In: Mathematische Annalen, 2004, vol. 330, no. 2, p. 293-308

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    Title
    • A conjecture of Beauville and Catanese revisited
    Author
    • Pink, Richard. Department of Mathematics, ETH-Zentrum, CH-8092, Zürich, Switzerland
    • Roessler, Damian. Department of Mathematics, ETH-Zentrum, CH-8092, Zürich, Switzerland
    Document Type
    • Postprint
    Classification
    • Mathematics
    OAI-PMH Identifier
    • oai:doc.rero.ch:322246
    Summary
    Abstract.: A theorem of Green, Lazarsfeld and Simpson (formerly a conjecture of Beauville and Catanese) states that certain naturally defined subvarieties of the Picard variety of a smooth projective complex variety are unions of translates of abelian subvarieties by torsion points. Their proof uses analytic methods. We refine and give a completely new proof of their result. Our proof combines galois-theoretic methods and algebraic geometry in positive characteristic. When the variety has a model over a function field and its Picard variety has no isotrivial factors, we show how to replace the galois-theoretic results we need by results from model theory (mathematical logic). Furthermore, we prove partial analogs of the conjecture of Beauville and Catanese in positive characteristic