Normal crossing properties of complex hypersurfaces via logarithmic residues

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, describe all free divisors with Gorenstein singular locus.

17 pages

References in corpus (1)

• Characterizing normal crossing hypersurfaces

Cited by in corpus (6)

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• Computing Regular Meromorphic Differential Forms via Saito's Logarithmic Residues
• K-theoretic defect in Chern class identity for a free divisor