ABSTRACT
Let K be an algebraically closed field of characteristic p>0. The aim of the article is to give a classification of simple parametrized plane curve singularities over K. The idea is to give explicitly a class of families of singularities which are not simple such that almost all singularities deform to one of those and show that remaining singularities are simple.
2010 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors would like to thank very much the referee for his helpful comments.
Notes
1Let and
two semigroups given by the minimal set of generators. We define
iff
or there exists i≤ min(l,k) such that
and
. In a deformation of a parametrization with semigroup Γ the semigroup is smaller or equal to Γ.
2The conductor of a semigroup is the minimum of all c in the semigroup such that all integers greater than c are in the semigroup.
3We assume as always that n<m and n∤m.
4Also called sagbi normal form.
5According to the definition of a deformation we are allowed to choose U with the property 0∈U as small as we need.