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for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.
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Is there a rigid curve in a product of complex manifolds?
Let $X=Y\times Z$ be a product of complex manifolds $Y,Z$. Is it true that there exists no rigid curve on $X$? Here I mean by a rigid curve a curve which is not a member of any family of curves on $X$ …