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Mathematische Annalen

, Volume 361, Issue 3–4, pp 995–1020 | Cite as

Characterizing normal crossing hypersurfaces

  • Eleonore FaberEmail author
Article

Abstract

The objective of this article is to give an effective algebraic characterization of normal crossing hypersurfaces in complex manifolds. It is shown that a divisor (=hypersurface) has normal crossings if and only if it is a free divisor, has a radical Jacobian ideal and a smooth normalization. Using K. Saito’s theory of free divisors, also a characterization in terms of logarithmic differential forms and vector fields is found. Finally, we give another description of a normal crossing divisor in terms of the logarithmic residue using recent results of M. Granger and M. Schulze.

Mathematics Subject Classification

32S25 32S10 32A27 14B04 

Notes

Acknowledgments

I thank my advisor Herwig Hauser for introducing me to this topic and for many comments and suggestions. I also thank David Mond, Luis Narváez and Mathias Schulze for several discussions, suggestions and comments. Moreover, ideas for this work originated from discussions with Alexander G. Aleksandrov, Michel Granger, Jan Schepers, Bernard Teissier and Orlando Villamayor, whose help shall be acknowledged.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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