The Milnor number of functions on singular hypersurfaces

• Autorzy: Mariusz Zając
• 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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 459-463

Daty

wydano

1996

Twórcy

autor

Mariusz Zając

• 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.