35 citations · 49 across the 8 of their papers we have counts for
8 papers
Equisingular Deformations of Plane Curves in Arbitrary Characteristic
Antonio Campillo, Gert-Martin Greuel, Christoph Lossen
In this paper we develop the theory of equisingular deformations of plane curve singularities in arbitrary characteristic. We study equisingular deformations of the parametrization…
Equisingular Families of Projective Curves
Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin
In this survey, we report on progress concerning families of projective curves with fixed number and fixed (topological or analytic) types of singularities. We are, in particular,…
Equisingular calculations for plane curve singularities
Antonio Campillo, Gert-Martin Greuel, Christoph Lossen
We present an algorithm which, given a deformation with trivial section of a reduced plane curve singularity, computes equations for the equisingularity stratum (that is, the mu-co…
A new Invariant for Plane Curve Singularities
Thomas Keilen, Christoph Lossen
Greuel, Lossen and Shustin gave a general sufficient numerical condition for the T-smoothness (smoothness and expected dimension) of equisingular families of plane curves. This con…
Castelnuovo function, zero-dimensional schemes and singular plane curves
Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin
We study families V of curves in P^2 of degree d having exactly r singular points of given topological or analytic types. We derive new sufficient conditions for V to be T-smooth (…
Plane curves of minimal degree with prescribed singularities
Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin
We prove that there exists a>0 such that for any integer d>2 and any topological types S_1,...,S_n of plane curve singularities, satisfying , there exi…