Dual logarithmic residues and free complete intersections

Details Dual logarithmic residues and free complete intersections Dual logarithmic residues and free complete intersections

2011-09-12

arxiv.org/abs/1109.2612v3

Mathematics

Algebraic Geometry

13 pages

Scientific paper

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 L\^e 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. We suggest a generalization of the notions of logarithmic vector fields and freeness for complete intersections. In the case of quasihomogeneous complete intersection space curves, we give an explicit description.

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