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YCor
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degeneration of coadjoint orbis

Let $X$ be a projecive manifold and we have a degeneration of fibers such that they are biholomorphic to coadjoint orbits, i.e, $X\to \Delta$ , and fibers $X_t$ are biholomorphic to coadjoint orbits then does $X_0$ biholomorphic to coadjoint orbit?

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