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Dual logarithmic residues and free complete intersections

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. 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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Preprints, Working Papers, ...
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Submitted on : Wednesday, January 11, 2012 - 10:43:42 PM
Last modification on : Wednesday, October 20, 2021 - 3:18:47 AM
Long-term archiving on: : Tuesday, December 13, 2016 - 10:32:43 PM


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  • HAL Id : hal-00656220, version 2



Michel Granger, Mathias Schulze. Dual logarithmic residues and free complete intersections. 2012. ⟨hal-00656220v2⟩



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