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$% A. Esterov, Indices of 1-forms and Newton polyhedra, Rev. Mat. Complut. 18
(2005), no. 1, 233–242.%$
Indices of 1-Forms and Newton Polyhedra
A formula of Matsuo Oka (1990) 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. In this paper this formula is generalized to the case of the index of a 1-form on a local complete intersection singularity (Theorem 1.10, corollaries 1.11, 4.1). In particular, the Newton polyhedron of a 1-form is defined (Definition 1.6). This also simplifies the Oka formula in some particular cases (Propositions 3.5, 3.7).
Key words: Newton polyhedra, singularities of vector fields.
2000 Mathematics Subject Classification: 32S65, 14M25.