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Journal Article

Deformations of categories of coherent sheaves via quivers with relations

MPS-Authors
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Barmeier,  Severin       
Max Planck Institute for Mathematics, Max Planck Society;

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Wang,  Zhengfang
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.14231/AG-2024-001
(Publisher version)

https://doi.org/10.48550/arXiv.2107.07490
(Preprint)

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Citation

Barmeier, S., & Wang, Z. (2024). Deformations of categories of coherent sheaves via quivers with relations. Algebraic Geometry, 11(1), 1-36. doi:10.14231/AG-2024-001.


Cite as: https://hdl.handle.net/21.11116/0000-000E-6923-5
Abstract
We give an explicit description of the deformation theory of the Abelian category of
(quasi-)coherent sheaves on any separated Noetherian scheme X via the deformation
theory of path algebras of quivers with relations, by using any affine open cover of X,
or any tilting bundle on X, if available.
We also give sufficient criteria for obtaining algebraizations of formal deformations,
in which case the deformation parameters can be evaluated to a constant and the
deformations can be compared to the original Abelian category on equal terms. We give
concrete examples as well as applications to the study of noncommutative deformations
of singularities.