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).
@article{urn:eudml:doc:44550,
title = {Indices of 1-forms and Newton polyhedra.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {18},
year = {2005},
pages = {233-242},
zbl = {1084.32024},
mrnumber = {MR2135540},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44550}
}
Esterov, Alexander. Indices of 1-forms and Newton polyhedra.. Revista Matemática de la Universidad Complutense de Madrid, Tome 18 (2005) pp. 233-242. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44550/