Equisingular Deformations of Plane Curve and of Sandwiched Singularities

Details Equisingular Deformations of Plane Curve and of Sandwiched Singularities Equisingular Deformations of Plane Curve and of Sandwiched Singularities

2000-11-15

arxiv.org/abs/math/0011097v2

Mathematics

Algebraic Geometry

19 pages, Latex, added references, added section

Scientific paper

Let $C$ be an isolated plane curve singularity, and $(C,l)$ be a decorated curve. In this article we compare the equisingular deformations of $C$ and the sandwiched singularity $X(C,l)$. We will prove that for $l \gg 0$ the functor of equisingular deformations of $C$ and $(C,l)$ are equivalent. From this we deduce a proof of a formula for the dimension of the equisingular stratum. Furthermore we will show how compute the equisingularity ideal of the curve singularity $C$, given the minimal (good) resolution of $C$.

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