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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-22,
author = {Guillaume Valette},
title = {Volume and multiplicities of real analytic sets},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {265-276},
zbl = {1092.32003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-22}
}
Guillaume Valette. Volume and multiplicities of real analytic sets. Annales Polonici Mathematici, Tome 85 (2005) pp. 265-276. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-22/