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- Title
Normal crossing properties of complex hypersurfaces via logarithmic residues.
- Authors
Granger, Michel; Schulze, Mathias
- Abstract
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.
- Subjects
HYPERSURFACES; LOGARITHMIC functions; MATHEMATICS theorems; ALGEBRA; MATHEMATICAL analysis; GORENSTEIN rings
- Publication
Compositio Mathematica, 2014, Vol 150, Issue 9, p1607
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X13007860