## 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

### Keywords:

Milnor number; equisingular family
Full Text:

### 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
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