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October 2022 Perverse sheaves on $\mathbf{C}^{2}$ without vanishing cycles at the origin along a general plane curve with singularities
Dérille Kouemo Djoukoue, Philibert Nang
Proc. Japan Acad. Ser. A Math. Sci. 98(8): 57-62 (October 2022). DOI: 10.3792/pjaa.98.011

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 $ \mathbf{C}^{2}$ 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.

Citation

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Dérille Kouemo Djoukoue. Philibert Nang. "Perverse sheaves on $\mathbf{C}^{2}$ without vanishing cycles at the origin along a general plane curve with singularities." Proc. Japan Acad. Ser. A Math. Sci. 98 (8) 57 - 62, October 2022. https://doi.org/10.3792/pjaa.98.011

Information

Published: October 2022
First available in Project Euclid: 29 September 2022

MathSciNet: MR4492078
zbMATH: 1504.32023
Digital Object Identifier: 10.3792/pjaa.98.011

Subjects:
Primary: 32C35
Secondary: 14F99 , 14H99 , 32C40

Keywords: algebraic link , fundamental group , local systems , perverse sheaves , Plane curve singularity

Rights: Copyright © 2022 The Japan Academy

Vol.98 • No. 8 • October 2022
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