Deformations of categories of coherent sheaves via quivers with relations

Severin Barmeier (University of Cologne, Germany)

12-May-2022, 11:00-12:00 (23 months ago)

Abstract: In this talk I will explain how to use the deformation theory of path algebras of quivers with relations to give a concrete and complete description of the deformation theory of the Abelian category coh(X) of coherent sheaves on any separated Noetherian scheme X. Deformations of coh(X) are a generous source of interesting examples of noncommutative schemes arising as an amalgamation of classical deformations of X, quantizations of Poisson structures on X and twists of the structure sheaf. Lowen and Van den Bergh showed that the deformation theory of coh(X) is equivalent to the deformation theory of a certain associative algebra, namely the "diagram algebra" associated to the restriction of the structure sheaf to any affine open cover. When X is Noetherian, this associative algebra and its deformations can be described concretely via a finite quiver with relations. This talk is based on arXiv:2107.07490 and arXiv:2002.10001 both joint with Zhengfang Wang.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

Comments: Meeting Link uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09

Meeting ID: 918 7552 8987 Password: LAGOON2022


Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

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Organizers: Severin Barmeier, Frank Neumann*, Sibylle Schroll*
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