SINGULAR Examples

Flatness

Genus

Application to Versal Deformations of Singularities

Problem:

Determine the strata of constant Tjurina number in the basis of a semiuniversal deformation of the hypersurface singularity given by f.

Let m₁,...,m_r be a monomial basis of the Tjurina algebra

T_local(f) = K[x,y]_<x,y> / < jacob(f), f >.

A semiuniversal deformation of f is then given by

F = f + t₁m₁ + ... + t_rm_r .

The relative T¹ of F,

is a finitely presentable K[t₁,...,t_r]-module. The strata of constant Tjurina number are just the flattening strata of this module.

Sao Carlos, 08/02