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Results tagged with complex-manifolds
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user 8003
For questions about or involving complex manifolds.
6
votes
Examples of non-Kähler compact complex manifolds which satisfy the Dolbeault isomorphism
I am slightly confused by Francesco's comment and answer, because the Frolicher spectral sequence does degenerate for compact complex surfaces. So why isn't a non-Kahler surface an example? Perhaps th …
- 1,493
4
votes
1
answer
243
views
“Logarithmic” form of Kodaira Embedding
Suppose you have a non-compact complex manifold $X$ with a Hodge metric, whose associated Kahler form has integral cohomology class. In the compact case, one would be able to conclude that $X$ is proj …
- 1,493
4
votes
1
answer
442
views
Exotic $\mathbb{R}^4$ with a complex structure?
Is there an exotic $\mathbb{R}^4$ admitting an integrable almost complex structure?
- 1,493
1
vote
Toroidal embedding
naf's comment is correct. This example can be seen as an instance of Mumford's construction of degenerations of abelian varieties into unions of toric varieties. Here is a "purely toric" construction …
- 1,493