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- Title
Deformations of categories of coherent sheaves via quivers with relations.
- Authors
Barmeier, Severin; Zhengfang Wang
- 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.
- Subjects
ALGEBRAIC geometry; SHEAF theory; ABELIAN categories; MATHEMATICAL singularities; RELATION algebras
- Publication
Algebraic Geometry, 2024, Vol 11, Issue 1, p1
- ISSN
2313-1691
- Publication type
Article
- DOI
10.14231/AG-2024-001