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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

Alexander ESTEROV
Faculty of Mechanics and Mathematics,
Moscow State University,
Moscow, GSP-2, 119992 -- Russia
esterov@mail.ru

Received: February 12, 2004
Accepted: October 4, 2004
ABSTRACT

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.