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Results tagged with complex-geometry
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user 9833
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.
9
votes
1
answer
366
views
Extending a holomorphic vector bundle: a reference request
Let $Y$ be a complex manifold, $X\subset Y$ a compact submanifold, and $E\to X$ a holomorphic vector bundle. Can $E$ be extended
to a bundle over an open neighborhood of $X$ in $Y$? (Four years a …
- 6,891
4
votes
1
answer
517
views
Adjusting the holomorphic structure of a vector bundle
Let $E\to X$ be a holomorphic vector bundle on a projective complex manifold. If $Y$ is another projective manifold diffeomorphic to $X$ then we are free to consider $E$ a smooth bundle over $ …
- 6,891
8
votes
1
answer
681
views
Extending the tangent bundle of a submanifold
Let $X$ be a complex manifold, and $Y\subset X$ a compact
submanifold. Is it true that the tangent bundle $TY$ may be
extended (as a holomorphic vector bundle) to some
open neighbourhood of $Y$ in …
- 6,891
7
votes
Accepted
Is complex analytic extension of real-analytic diffeomorphism a diffeomorphism ?
Indeed, a real-analytic map can always be extended to some complex neighbourhood.
The problem is, the neighbourhood may be very small. Consider, for example,
the map
$$f:I\to I,\, I=[-1,1],$$
define …
- 6,891