Dual logarithmic residues and free complete intersections

Michel Granger (1) , Mathias Schulze (2)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 OU - University of Oklahoma

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. 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.

Mots clés: Differential form; residue; duality; free divisor; complete intersection; complete intersection.

Domaines: Géométrie algébrique [math.AG]

Michel Granger, Mathias Schulze. Dual logarithmic residues and free complete intersections. 2012. ⟨hal-00656220v1⟩