Resumen de Indices of 1-forms and Newton polyhedra

Alexander Esterov

• A formula of Matsuo Oka [9] expresses the Milnor number of a germ of a complex analytic map with a generic principal part in terms of the Newton polyhedra of the components of the map. So this paper this formula is generalized to the case of the index of a 1-form no a local complete intersection singularity (Theorem 1.10, Corollaries 1.11, 4.1). In particular, the Newton polyhedron of a l-form is defined (Definition 1.6). This also simplifies the Oka formula in some particular cases (Propositions 3.5, 3.7).