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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.

2 votes

$(-2)$-curves in complex $3$-folds

Yes, this result appeared in "Uber Modifikationen und exzeptionelle analytische Mengen" (Mathematische Annalen, vol. 146, n.4) by H. Grauert. See the Corollary on p. 363, which also treats a much more …
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6 votes
1 answer
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$(-2)$-curves in complex $3$-folds

Let $X$ be a smooth complex $3$-fold, and let $C \subset X$ be an embedded smooth rational curve whose normal bundle $N_{C/X}$ is isomorphic to $\mathscr{O}(-1) \oplus \mathscr{O}(-1)$. Is it true …
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