Antonio Campillo López (Universidad de Valladolid, España (Spain))

Title: COMPUTING EQUIPOLYGONAL STRATA


Equisingularity of plane curve singularities can be understood as 
equipolygonality at each step of their resolution of singularities processes. 
Equipolygonal deformations are those which preserve adapted (to created 
exceptional divisors) Newton polygons. Functors of equipolygonal deformations 
modulo adapted isomorphisms become smooth ones. We show how versality 
equipolygonal deformations is preserved under blow ups. The proof is an 
effective one and based on computer algebra methods, and it stands over fields 
of any characteristic. Algorithms to compute equipolygonal strata are derived. 
They can be used to compute curve equisingular strata and to prove statements 
on strata smoothness. This is joint reserach with G.M.Greuel and Ch.Lossen.