×

An example concerning a question of Zariski. (English) Zbl 0605.14013

Let f(x,y,z,t) be an analytic function such that for each t fixed, \(f=0\) defines a surface with isolated singularity at the origin with the same Milnor number \((=equi\sin gular)\). The author gives an example of such a family with the following property: The generic projection is not equisingular but there is a transverse projection which gives an equisingular family.
Reviewer: M.Oka

MSC:

14E15 Global theory and resolution of singularities (algebro-geometric aspects)
32S05 Local complex singularities
14B05 Singularities in algebraic geometry
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML

References:

[1] BRIANÇON (J.) et HENRY (J.-P. G.) . - Equisingularité générique des familles des surfaces à singularités isolées , Bull. Soc. Math. Fr., vol. 108, 1980 , p. 260-284. Numdam | MR 82j:14007 | Zbl 0482.14004 · Zbl 0482.14004
[2] BRIANÇON (J.) et SPEDER (J.-P.) . - Familles équisingulières de surfaces à singularité isolée , C.R. Acad. Sc., t. 280, série A, 1975 , p. 1013-1016. MR 55 #712 | Zbl 0312.14005 · Zbl 0312.14005
[3] BRIANÇON (J.) et SPEDER (J. P.) . - Familles équisingulières d’hypersurfaces à singularité isolée , Thèse 2e partie, Nice, 1976 .
[4] TEISSIER (B.) . - Proof that Zariski dimensional type can be computed with linear projections, when it is \?2 . Notes of Lectures at the Harvard Singularities Seminar. 1981 .
[5] ZARISKI (O.) . - Some open question in the theory of singularities , Bull. A.M.S., vol. 77, n^\circ 4, 1971 , p. 481-491. Article | MR 43 #3266 | Zbl 0236.14002 · Zbl 0236.14002
[6] ZARISKI (O.) . - On the elusive concept of equisingularity , Symposium in Honor to J. Silvester, Johns Hopkins Univ. Press, Baltimore, 1978 . · Zbl 0422.14006
[7] ZARISKI (O.) . - Foundations of a general theory of equisingularity on r-dimensional algebroid and algebraic varieties embedding dimension r + 1 , Amer. J. Math., 101, 2, 1979 , p. 453-514. MR 81m:14005 | Zbl 0417.14008 · Zbl 0417.14008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.