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Results tagged with cv.complex-variables
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user 13168
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
10
votes
0
answers
347
views
Analytic space not embeddable in any complex manifold
I am looking for an example of a compact complex analytic space, reduced and irreducible, which does not admit any holomorphic embedding into any (smooth) complex manifold (possibly non-compact).
I a …
- 6,871
32
votes
2
answers
2k
views
Example of a compact Kähler manifold with non-finitely generated canonical ring?
A celebrated recent theorem of Birkar-Cascini-Hacon-McKernan and Siu says that the canonical ring $R(X)=\oplus_{m\geq 0}H^0(X,mK_X)$ of any smooth algebraic variety $X$ over $\mathbb{C}$ is a finitely …
- 6,871
37
votes
1
answer
3k
views
Is S^2 x S^4 a complex manifold?
As observed by Calabi a long time ago, the manifold $S^2\times S^4$ admits an almost-complex structure (obtained by embedding it in $\mathbb{R}^7$ and using the octonionic product), which however is n …
- 6,871