The behaviour of a holomorphic map germ at a critical point has always been an important part of the singularity theory. It is generally known (cf. [5]) that we can associate an integer invariant - called the multiplicity - to each isolated critical point of a holomorphic function of many variables. Several years later it was noticed that similar invariants exist for function germs defined on isolated hypersurface singularities (see [1]). The present paper aims to show a simple approach to critical points of maps defined on the -type singular hypersurfaces. After some changes it can probably be adopted to other isolated hypersurface singularities.
@article{bwmeta1.element.bwnjournal-article-bcpv33z1p459bwm,
author = {Zaj\k ac, Mariusz},
title = {The Milnor number of functions on singular hypersurfaces},
journal = {Banach Center Publications},
volume = {37},
year = {1996},
pages = {459-463},
zbl = {0855.32017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p459bwm}
}
Zając, Mariusz. The Milnor number of functions on singular hypersurfaces. Banach Center Publications, Tome 37 (1996) pp. 459-463. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p459bwm/
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[002] [3] V. P. Palamodov, Multiplicity of holomorphic mappings, Funct. Anal. Appl. 1 (1967), 218-266.
[003] [4] J. Milnor, Singular Points of Complex Hypersurfaces, Ann. of Math. Stud. 61, Princeton Univ. Press, 1968. | Zbl 0184.48405
[004] [5] P. Orlik, The multiplicity of a holomorphic map at an isolated critical point, in: P. Holm (ed.), Real and Complex Singularities, Proc. Nordic Summer School/NAVF, Oslo 1976, Sijthoff & Noordhoff, 1977, 405-474.