The Aluﬃ algebra of hypersurfaces with isolated singularities. Issue 8 (3rd August 2018) - Nasrollah Nejad, Abbas
ABSTRACT: The Aluﬃ algebra is an algebraic definition of a characteristic cycle of a hypersurface in intersection theory. In this paper, we study the Aluﬃ algebra of quasi-homogeneous and locally Eulerian hypersurfaces with only isolated singularities. We prove that the Jacobian ideal of an aﬃne hypersurface with isolated singularities is of linear type if and only if it is locally Eulerian. We show that the gradient ideal of a projective hypersurface with only isolated singularities is of linear type if and only if the aﬃne curve in each aﬃne chart associated to singular points is locally Eulerian. We show that the gradient ideal of Nodal and Cuspidal projective plane curves are of linear type.