To a given complex-analytic equidimensional corank-1 germ f, one can associate a set of integer 𝓐-invariants such that f is 𝓐-finite if and only if all these invariants are finite. An analogous result holds for corank-1 germs for which the source dimension is smaller than the target dimension.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-18,
author = {Joachim H. Rieger},
title = {Invariants of equidimensional maps},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {239-248},
zbl = {1072.32019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-18}
}
Joachim H. Rieger. Invariants of equidimensional maps. Banach Center Publications, Tome 60 (2003) pp. 239-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-18/