Isolated line singularities

Siersma, Dirk

doi:10.1090/pspum/040.2/713274

Cited by 73 publications

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“…In [22], Siersma proved another closely related result, at the homotopy level. On the level of homology, what he proved was that, if f is not Milnor equisingular, and Σf has a single smooth component, ν, such that…”

Section: Thus the Rank Ofmentioning

confidence: 94%

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Hypersurface Singularities and Milnor Equisingularity

Massey¹,

Tráng²

2006

Pure and Applied Mathematics Quarterly

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Section: Thus the Rank Ofmentioning

confidence: 94%

“…Finally, as we mentioned earlier, while our result is on the homology level, one may also investigate this situation on the homotopy level, as in [22] (in the case λ 1 f,z 0 (0) = 1) and in [30] (in the general s = 1 case). The homology statement in Theorem 5.1 follows from these homotopy results.…”

mentioning

confidence: 90%

Hypersurface Singularities and Milnor Equisingularity

Massey¹,

Tráng²

2006

Pure and Applied Mathematics Quarterly

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“…In what follows, just as in [3], [4], [8] and [9], the study will be limited to elements f of I 2 . Beside technical considerations, the preceding lemma provides a motivation for this approach.…”

Section: Non-isolated Singularities Letmentioning

confidence: 99%

Infinite determinacy on a closed set for smooth germs with non-isolated singularities

Thilliez¹

2005

Proc. Amer. Math. Soc.

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Abstract. We give necessary and sufficient conditions for infinite determinacy of a smooth function germ whose critical locus contains a given set. This set is assumed to be the zero variety X of some analytic map-germ having maximal rank on a dense subset of X. We obtain a result in terms of Lojasiewicz estimates which extends, in particular, previous works by Sun and Wilson on line singularities, and by Grandjean on singularities of codimension 1 or 2.

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“…. (see for example [5], [8], [9], [10], [13], [14], [15], [20]). Many of these papers use a generalized morsification method that consists in de-…”

Section: Introductionmentioning

confidence: 99%

Topological finite-determinacy of functions with non-isolated singularities

Bobadilla¹

2004

Comment. Math. Helv.

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Abstract.We introduce the concept of topological finite-determinacy for germs of analytic functions within a fixed ideal I, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We prove the following statement which generalizes classical results of Thom and Varchenko: let A be the complement in the ideal I of the space of germs whose topological type remains unchanged under a deformation within the ideal that only modifies sufficiently large order terms of the Taylor expansion. Then A has infinite codimension in I in a suitable sense. We also prove the existence of generic topological types of families of germs of I parametrized by an irreducible analytic set. Mathematics Subject Classification (2000). Primary 32S15, 58K40.

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Isolated line singularities

Cited by 73 publications

References 0 publications

Hypersurface Singularities and Milnor Equisingularity

Hypersurface Singularities and Milnor Equisingularity

Infinite determinacy on a closed set for smooth germs with non-isolated singularities

Topological finite-determinacy of functions with non-isolated singularities

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