## EQUISINGULAR DEFORMATIONS OF PLANE CURVES IN ARBITRARY CHARACTERISTIC (2006)

### BibTeX

@MISC{Campillo06equisingulardeformations,

author = {Antonio Campillo and Gert-martin Greuel and Christoph Lossen},

title = {EQUISINGULAR DEFORMATIONS OF PLANE CURVES IN ARBITRARY CHARACTERISTIC},

year = {2006}

}

### OpenURL

### Abstract

Dedicated to Joseph Steenbrink on the occasion of his sixtieth birthday Abstract. In this paper we develop the theory of equisingular deformations of plane curve singularities in arbitrary characteristic. We study equisingular deformations of the parametrization and of the equation and show that the base space of its semiuniveral deformation is smooth in both cases. Our approach through deformations of the parametrization is elementary and we show that equisingular deformations of the parametrization form a linear subfunctor of all deformations of the parametrization. This gives additional information, even in characteristic zero, the case which was treated by J. Wahl. The methods and proofs extend easily to good characteristic, that is, when the characteristic does not divide the multiplicity of any branch of the singularity. In bad characteristic, however, new phenomena occur and we are naturally led to consider weakly trivial respectively weakly equisingular deformations, that is, those which become trivial respectively equisingular after a finite and dominant base change. The semiuniversal base space for weakly equisingular

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