On the quotient of Milnor and Tjurina numbers for two-dimensional isolated hypersurface singularities

Patricio Almirón

Published 2019-10-28Version 1

We improve the known upper bound for the quotient of the Milnor number and Tjurina number for some families of isolated complete intersection surface singularities and we conjecture that this bound would be valid for any isolated hypersurface singularity of dimension two. As a consequence, we give a positive answer to a question of Dimca and Greuel about this quotient in the case of plane curve singularities.