A theorem on the existence of a maximal analytic family of surfaces with ordinary singularities in the projective 3-space. (English) Zbl 0667.14016
Let S be a surface of order n in \({\mathbb{P}}^ 3\) with only ordinary singularities along a double curve \(\Delta\). Assume that the infinitesimal locally trivial deformations of \(\Delta\) are unobstructed. It is shown that for n bigger than a number computable in terms of \(\Delta\) only also the locally trivial deformations of S are unobstructed.
Reviewer: H.Knörrer
MSC:
| 14J17 | Singularities of surfaces or higher-dimensional varieties |
| 32S30 | Deformations of complex singularities; vanishing cycles |
| 14D15 | Formal methods and deformations in algebraic geometry |
| 14B05 | Singularities in algebraic geometry |
| 14B07 | Deformations of singularities |
