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for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.
24
votes
Accepted
Almost Complex Structure approach to Deformation of Compact Complex Manifolds
This approach to deformations is taken, for instance, in all of the original papers of Kodaira-Spencer and Nirenberg. You can have a look at
On the existence of deformations of complex analytic st …
8
votes
Algebraic definition of the Kuranishi map
In characteristic zero the answer is positive.
If $L^\bullet$ is the dgla (differential graded Lie algebra) governing your deformation problem (the Kodaira-Spencer dgla $\oplus A^{0,p}(X,T_X)$ in your …