Abstract:
Generalizing MacPherson-Vilonen’s method [2] to arbitrary plane curve
singularities, we provide a classification of perverse sheaves on the neighborhood of the origin
in the complex plane, which are adapted to a germ of a complex analytic plane curve. We rely on
the presentation of the fundamental group of the complement of the curve as obtained by Neto
and Silva [5]. The main result is an equivalence of categories between the category of perverse
sheaves on C2 stratified with respect to a singular plane curve and the category of n-tuples of
finite dimensional vector spaces and linear maps satisfying a finite number of suitable relations.
As an application, we classify perverse sheaves with no vanishing cycles at the origin for a special
case.
