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3 results

  • Normal crossing properties of complex hypersurfaces via logarithmic residues

  • Part of
  • Michel Granger, Mathias Schulze
  • Journal:
    Compositio Mathematica / Volume 150 / Issue 9 / September 2014
    Published online by Cambridge University Press:
    25 June 2014, pp. 1607-1622
    Print publication:
    September 2014
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  • We introduce a dual logarithmic residue map for hypersurface singularities and use it to answer a question of Kyoji Saito. Our result extends a theorem of Lê and Saito by an algebraic characterization of hypersurfaces that are normal crossing in codimension one. For free divisors, we relate the latter condition to other natural conditions involving the Jacobian ideal and the normalization. This leads to an algebraic characterization of normal crossing divisors. As a side result, we describe all free divisors with Gorenstein singular locus.

  • Variétés Singulières et Extension des Fonctions Holomorphes

  • Vincent Duquenoy, Emmanuel Mazzilli
  • Journal:
    Nagoya Mathematical Journal / Volume 192 / 2008
    Published online by Cambridge University Press:
    11 January 2016, pp. 151-167
    Print publication:
    2008
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  • In this paper, we study a problem of extension of holomorphic functions given on a complex hypersurface with singularities on the boundary of a strictly pseudoconvex domain.

  • Residue Integrals and their Mellin Transforms

  • Mikael Passare, August Tsikh
  • Journal:
    Canadian Journal of Mathematics / Volume 47 / Issue 5 / 01 October 1995
    Published online by Cambridge University Press:
    20 November 2018, pp. 1037-1050
    Print publication:
    01 October 1995
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  • Given an almost arbitrary holomorphic map we study the structure of the associated residue integral and its Mellin transform, and the relation between these two objects. More precisely, we relate the limit behaviour of the residue integral to the polar structure of the Mellin transform. We consider also ideals connected to nonisolated singularities.