On resolution complexity of plane curves (Q1902047)

The authors show that any isolated plane curve singular point can be resolved in a sequence of toroidal blowing-ups. They prove that the minimal number of required toroidal blowing-ups is a topological invariant depending on the number of local branches and number of Puiseux pairs of each branch. That minimal number is called resolution complexity. -- The behavior of the resolution complexity for singular points of hypersurfaces and its connection with complexity of plane sections are stated as open problems.