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for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.
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Are singular rational curves on K3 surfaces rigid?
Let $S$ be a K3 surface over the complex numbers $\mathbb{C}$. If $C\subset S$ is a smooth rational curve, the normal bundle $N_{C/S}$ is isomorphic to $\mathbb{O}(-2)$ and thus $C$ is rigid. What abo …