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Results tagged with complex-geometry
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user 135047
Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
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 …
- 81
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 …
- 81