Abstract
Let \({g: (\mathbb{C}^n, 0)\to (\mathbb{C}^n, 0)}\) be a finite analytic map. We give an expression for the local Łojasiewicz exponent and for the multiplicity of g when the component functions of g satisfy certain condition with respect to a set of n monomial ideals I 1,..., I n . We give an effective method to compute Łojasiewicz exponents based on the computation of mixed multiplicities. As a consequence of our study, we give a numerical characterization of a class of functions that includes semi-weighted homogenous functions and Newton non-degenerate functions.
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Work supported by DGICYT Grant MTM2006-06027.
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Bivià-Ausina, C. Local Łojasiewicz exponents, Milnor numbers and mixed multiplicities of ideals. Math. Z. 262, 389–409 (2009). https://doi.org/10.1007/s00209-008-0380-z
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DOI: https://doi.org/10.1007/s00209-008-0380-z
Keywords
- Milnor number
- Łojasiewicz exponents
- Integral closure of ideals
- Mixed multiplicities of ideals
- Newton polyhedra