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for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.
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first order deformation of maps and curves preserving dual graph
suppose that $\mu:C \to X$ be pointed stable map and $G$ be the dual graph of $C$.
Fulton and Pandharipande in their paper,FP_notes,define two linear spaces $Def_G(\mu) \subset Def(\mu)$ as first ord …