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Normal crossing properties of complex hypersurfaces via logarithmic residues

Part of:SingularitiesHolomorphic functions of several complex variablesAnalytic spaces

Published online by Cambridge University Press:  25 June 2014

Michel Granger and
Mathias Schulze
Michel Granger
Affiliation:
Université d’Angers, Département de Mathématiques, LAREMA, CNRS UMR 6093, 2 Bd Lavoisier, 49045 Angers, France email granger@univ-angers.fr
Mathias Schulze
Affiliation:
Department of Mathematics, University of Kaiserslautern, 67663 Kaiserslautern, Germany email mschulze@mathematik.uni-kl.de
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Abstract

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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.

Keywords

logarithmic residuedualityfree divisornormal crossing

MSC classification

Secondary:32A27: Local theory of residues32C37: Duality theorems32S25: Surface and hypersurface singularities

Information

Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 9 , September 2014, pp. 1607 - 1622
Copyright
© The Author(s) 2014 

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