Tjurina number

Summary

The Tjurina number of an isolated hypersurface singularity is the dimension of the space of its first-order deformations up to coordinate changes. It is the number of parameters of a miniversal deformation of the hypersurface germ. It is computed from the defining function and its partial derivatives, and it is at most the Milnor number. K. Saito proved that the two numbers are equal exactly when the function is quasi-homogeneous in suitable coordinates.