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Mixed Newton numbers and isolated complete intersection singularities
Author(s) -
BiviàAusina Carles
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm003
Subject(s) - mathematics , intersection (aeronautics) , gravitational singularity , complete intersection , newton's method , combinatorics , mathematical analysis , geography , cartography , physics , nonlinear system , quantum mechanics
Let f :(ℂ n , 0) → (ℂ p , 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.