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/