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

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dc.contributor.author Djoukoue, Derille Kouemo
dc.contributor.author Nang, Philibert
dc.date.accessioned 2023-10-27T08:29:32Z
dc.date.available 2023-10-27T08:29:32Z
dc.date.issued 2022-10
dc.description.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. en_US
dc.description.department Mathematics and Applied Mathematics en_US
dc.description.librarian am2023 en_US
dc.description.sponsorship The NLAGA project. en_US
dc.description.uri https://www.japan-acad.go.jp/en/publishing/pja_a.html en_US
dc.identifier.citation DjouKoue, 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. en_US
dc.identifier.issn 0386-2194
dc.identifier.other 10.3792/pjaa.98.011
dc.identifier.uri http://hdl.handle.net/2263/93099
dc.language.iso en en_US
dc.publisher Japan Academy en_US
dc.rights © 2022 The Japan Academy. This article is published open access. en_US
dc.subject Perverse sheaves en_US
dc.subject Local systems en_US
dc.subject Plane curve singularity en_US
dc.subject Fundamental group en_US
dc.subject Algebraic link en_US
dc.title Perverse sheaves on C2 without vanishing cycles at the origin along a general plane curve with singularities en_US
dc.type Article en_US


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