The Milnor number of functions on singular hypersurfaces

Mariusz Zając

Banach Center Publications (1996)

  • Volume: 33, Issue: 1, page 459-463
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Zając, Mariusz. "The Milnor number of functions on singular hypersurfaces." Banach Center Publications 33.1 (1996): 459-463. <http://eudml.org/doc/262874>.

@article{Zając1996,
abstract = {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.},
author = {Zając, Mariusz},
journal = {Banach Center Publications},
keywords = {Milnor number; functions on hypersurfaces; algebraic multiplicity},
language = {eng},
number = {1},
pages = {459-463},
title = {The Milnor number of functions on singular hypersurfaces},
url = {http://eudml.org/doc/262874},
volume = {33},
year = {1996},
}

TY - JOUR
AU - Zając, Mariusz
TI - The Milnor number of functions on singular hypersurfaces
JO - Banach Center Publications
PY - 1996
VL - 33
IS - 1
SP - 459
EP - 463
AB - 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.
LA - eng
KW - Milnor number; functions on hypersurfaces; algebraic multiplicity
UR - http://eudml.org/doc/262874
ER -

References

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  1. [1] A. Dimca, Function germs defined on isolated hypersurface singularities, Compositio Math. 53 (1984), 245-258. Zbl0548.32005
  2. [2] A. G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor, Invent. Math. 32 (1976), 1-31. 
  3. [3] V. P. Palamodov, Multiplicity of holomorphic mappings, Funct. Anal. Appl. 1 (1967), 218-266. 
  4. [4] J. Milnor, Singular Points of Complex Hypersurfaces, Ann. of Math. Stud. 61, Princeton Univ. Press, 1968. Zbl0184.48405
  5. [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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