For every smooth cubic in P^2, a dense G_delta set of 9-point blowup configurations yields a non-linearizable strict transform with nontorsion normal bundle.
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Affine closure of T*O_n in sl_n is isomorphic via C*-Hamiltonian reduction to the minimal nilpotent orbit closure in so_{2n+2}, and has no symplectic resolution.
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Nonlinearizable embeddings of elliptic curves in rational surfaces
For every smooth cubic in P^2, a dense G_delta set of 9-point blowup configurations yields a non-linearizable strict transform with nontorsion normal bundle.
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A connection between minimal nilpotent orbits of types A and D via Hamiltonian reduction
Affine closure of T*O_n in sl_n is isomorphic via C*-Hamiltonian reduction to the minimal nilpotent orbit closure in so_{2n+2}, and has no symplectic resolution.