In this talk, we study the nilpotent part of a pseudo-periodic automorphism of a real oriented
surface with boundary. We associate a quadratic form Q defined on the first homology group of the surface.
Using some techniques from mapping class group theory, we prove that a related form is positive
definite under some conditions that are always satisfied for monodromies of Milnor fibers of germs of curves on
normal surface singularities. Moreover, the form Q is computable in terms of the dual resolution or semistable reduction graph.
Numerical invariants associated with Q are able to distinguish plane curve singularities with different topological
types but same spectral pairs. This is a joint work with L. Alanís, E. Artal, C. Bonatti, X. Gómez-Mont and M. González Villa.