Djoukoue, Derille KouemoNang, Philibert2023-10-272023-10-272022-10DjouKoue, D.K. & Nang, P. 2022, 'Perverse sheaves on C2 without vanishing cycles at the origin along a general plane curve with singularities', Proceedings of the Japan Academy Series A: Mathematical Sciences, vol. 98, no. 8, pp. 57-62. http://dx.DOI.org/10.3792/pjaa.98.011.0386-219410.3792/pjaa.98.011http://hdl.handle.net/2263/93099Generalizing 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.en© 2022 The Japan Academy. This article is published open access.Perverse sheavesLocal systemsPlane curve singularityFundamental groupAlgebraic linkArticle