Deformation theory of objects in homotopy and derived categories III: abelian categories
arXiv:math/0702840 · doi:10.1016/j.aim.2010.11.003
Abstract
This is the third paper in a series. In part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to study deformations of objects in homotopy and derived categories of abelian categories. Then we consider examples from (noncommutative) algebraic geometry. In particular, we study noncommutative Grassmanians that are true noncommutative moduli spaces of structure sheaves of projective subspaces in projective spaces.
Alexander Efimov is a new co-author of this paper. Besides some minor changes, a new part (part 3) about noncommutative Grassmanians was added
References in corpus (4)
Cited by in corpus (13)
- Noncommutative deformations and flops
- Smoothness of equivariant derived categories
- Deformation theory of objects in homotopy and derived categories I: general theory
- Deformation theory of objects in homotopy and derived categories II: pro-representability of the deformation functor
- Gopakumar-Vafa invariants and wall-crossing
- Purity and 2-Calabi-Yau categories
- The derived deformation theory of a point
- The derived contraction algebra
- Non-commutative thickening of moduli spaces of stable sheaves
- Regular subcategories in bounded derived categories of affine schemes
- Non-commutative virtual structure sheaves
- Noncommutative Grassmannian of codimension two has coherent coordinate ring
- Coherence of relatively quasi-free algebras