Perverse sheaves on C2 without vanishing cycles at the origin along a general plane curve with singularities

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.The NLAGA project.https://www.japan-acad.go.jp/en/publishing/pja_a.htmlam2023Mathematics and Applied Mathematic

On the classification of regular holonomic D-modules on skew-symmetric matrices

AbstractWe give a classification of regular holonomic D-modules on 2m×2m-skew-symmetric matrices related to the action of the general linear group GL(2m,C). Actually we establish one more case of the conjecture by T. Levasseur (Levasseur, 2009 [12, p. 508, Conjecture 5.17])

Nonlinear Analysis, Geometry and Applications : Proceedings of the First NLAGA-BIRS Symposium

This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24–28, 2019. The four-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems. The book addresses a range of topics related to partial differential equations, geometrical analysis of optimal shapes, geometric structures, optimization and optimal transportation, control theory, and mathematical modeling