Parameswaran, A. J.
(1991)
*Topological equisingularity for isolated complete intersection singularities*
Compositio Mathematica, 80
(3).
pp. 323-336.
ISSN 0010-437X

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## Abstract

Let X, x be a germ of an analytic variety (over the complex numbers) which is a complete intersection isolated singularity. The author associates to X, x a sequence µ^{∗}= (µ_{0}, µ_{1}, . . . ) of numerical invariants by taking µ^{i} to be the minimal value of the Milnor numbers µ(X_{i}, x_{i}) for all deformations (X_{i}, x_{i}) → (S_{i}, s_{i}) of X, x with dim S_{i} = i. One has µ_{0} = µ(X, x) and µ_{i} = 0 if i is bigger than the embedding codimension of X, x. On the other hand the author defines the topological type of X, x as the class of homeomorphism of any sequence of germs (X, x) = (X_{0}, x) ⊂ (X_{1}, x) ⊂ ... ⊂ (X_{k}, x) where k is the embedding codimension of X, x, for each i, µ(X_{i}, x) = µ_{i}(X, x) and then the homeomorphism class does not depend on the X_{i}. The main result in the paper says that a µ^{∗}-constant family of isolated complete intersection singularities of dimension different from two is topologically equisingular. A sufficient condition for the members of the family to have isomorphic monodromy fibrations is also given.

Item Type: | Article |
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Source: | Copyright of this article belongs to Cambridge University Press. |

Keywords: | Equisingularity; Topological Type of Singularity; Complete Intersection Isolated Singularity; Milnor Numbers; Isomorphic Monodromy Fibrations |

ID Code: | 87685 |

Deposited On: | 20 Mar 2012 14:07 |

Last Modified: | 20 Mar 2012 14:07 |

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