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Banach Center Publications

1996 | 33 | 1 | 459-463
Tytuł artykułu

The Milnor number of functions on singular hypersurfaces

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $A_k$-type singular hypersurfaces. After some changes it can probably be adopted to other isolated hypersurface singularities.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
459-463
Opis fizyczny
Daty
wydano
1996
Twórcy
autor
• Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland
Bibliografia
• [1] A. Dimca, Function germs defined on isolated hypersurface singularities, Compositio Math. 53 (1984), 245-258.
• [2] A. G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor, Invent. Math. 32 (1976), 1-31.
• [3] V. P. Palamodov, Multiplicity of holomorphic mappings, Funct. Anal. Appl. 1 (1967), 218-266.
• [4] J. Milnor, Singular Points of Complex Hypersurfaces, Ann. of Math. Stud. 61, Princeton Univ. Press, 1968.
• [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.
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Bibliografia
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