Variétés polaires, stratifications de Whitney et classes de Chern des espaces analytiques complexes
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Volume and multiplicities of real analytic sets
Guillaume Valette (2005)
Annales Polonici Mathematici
We give criteria of finite determinacy for the volume and multiplicities. Given an analytic set described by {v = 0}, we prove that the log-analytic expansion of the volume of the intersection of the set and a "little ball" is determined by that of the set defined by the Taylor expansion of v up to a certain order if the mapping v has an isolated singularity at the origin. We also compare the cardinalities of finite fibers of projections restricted to such a set.
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