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2 results

  • Représentations linéaires des groupes kählériens : factorisations et conjecture de Shafarevich linéaire

  • Part of
  • Fréderic Campana, Benoît Claudon, Philippe Eyssidieux
  • Journal:
    Compositio Mathematica / Volume 151 / Issue 2 / February 2015
    Published online by Cambridge University Press:
    26 November 2014, pp. 351-376
    Print publication:
    February 2015
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  • We extend to compact Kähler manifolds some classical results on linear representation of fundamental groups of complex projective manifolds. Our approach, based on an interversion lemma for fibrations with tori versus general type manifolds as fibers, gives a refinement of the classical work of Zuo. We extend to the Kähler case some general results on holomorphic convexity of coverings such as the linear Shafarevich conjecture.

  • Holomorphic Generation of Continuous Inverse Algebras

  • Harald Biller
  • Journal:
    Canadian Journal of Mathematics / Volume 59 / Issue 1 / 01 February 2007
    Published online by Cambridge University Press:
    20 November 2018, pp. 3-35
    Print publication:
    01 February 2007
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  • We study complex commutative Banach algebras (and, more generally, continuous inverse algebras) in which the holomorphic functions of a fixed $n$-tuple of elements are dense. In particular, we characterize the compact subsets of ${{\mathbb{C}}^{n}}$ which appear as joint spectra of such $n$ -tuples. The characterization is compared with several established notions of holomorphic convexity by means of approximation conditions.