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Proceedings of the London Mathematical Society Advance Access originally published online on March 22, 2007
Proceedings of the London Mathematical Society 2007 94(3):749-771; doi:10.1112/plms/pdm003
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© 2007 London Mathematical Society

Mixed Newton numbers and isolated complete intersection singularities

Carles Bivià-Ausina

Departament de Matemàtica Aplicada
Universitat Politècnica de València
ETSGE
Camí de Vera, s/n
46022 València
Spain
carbivia{at}mat.upv.es

Received 15 February 2006. Revision received 6 September 2006.

Let f:(Cn, 0) -> (Cp, 0) be a complete intersection with an isolated singularity at the origin. We give a lower bound for the Milnor number of f in terms of the mixed multiplicities of a set of monomial ideals attached to the Newton polyhedra of the component functions of f. The Milnor number of f equals the bound that we give when f satisfies a condition that we define and that extends the notion of Newton non-degenerate function studied by Kouchnirenko. Our techniques are based on the notion of integral closure of submodules and its relation with Buchsbaum–Rim multiplicity and mixed multiplicities of a set of ideals.


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