# The Milnor number of functions on singular hypersurfaces

Banach Center Publications (1996)

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

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topZając, 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

top- [1] A. Dimca, Function germs defined on isolated hypersurface singularities, Compositio Math. 53 (1984), 245-258. Zbl0548.32005
- [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. Zbl0184.48405
- [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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