In this work, we study the cellular decomposition of S induced by a filling pair curves v and w, \(Dec_{v,w}(S) = {\setminus } (v \cup w)\), its connection to distance function d(v, w) in curve graph closed orientable surface genus g. Building on work Leasure, efficient geodesics were introduced first author joint with Margalit Menasco 2016, giving an algorithm that begins non-separating determ...

In this paper we give a positive answer to question of Dimca and Greuel about the quotient between Milnor Tjurina numbers for any irreducible germ plane curve singularity. This result is based on closed formula minimal number an equisingularity class in terms sequence multiplicities strict transform along resolution. The key points proof are previous results by Genzmer, Wall Mattei.