All Questions
Tagged with foliations complex-geometry
5 questions
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Understanding $\mathcal G$ in $\Bbb C$.
Construction:
Define $\mathcal F$ by the union of leaves:
$$\mathcal F:=\bigg \lbrace \mathcal M[\chi_t(x)]\cup \mathcal M\bigg[\frac{1}{1-\chi_r(x)}\bigg] \bigg \rbrace$$
where $\mathcal M$ denotes ...
- 204
1
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55
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Foliation by complex hypersurfaces
I am learning about the Levi flat hypersurfaces. Let $M \subseteq \mathbb{C}^n$ be a real smooth hypersurface, i.e. for every point $p$ in $M$ there is an open set $U_p$ in $\mathbb{C}^n$ containing $...
- 1,025
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177
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Line bundle associated with a $1$-cocyle of holomorphic functions.
I'm trying to understand the following extract:
A holomorphic foliation by curves $\mathcal{F}$ of degree $r$ on the projective space is a bundle map $\Omega : H_{-r+1} \rightarrow T\mathbb{P}^n$, ...
- 2,545
4
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56
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foliation with many tangencies
Suppose you have smooth foliation on a Euclidean ball $\mathbb{B}^{4} \subset \mathbb{C}^{2}$, whose leaves are holomorphic curves with respect to the standard complex structure. Let $(z_{1},z_{2})$ ...
- 4,460
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Proper surjective holomorphic function is a topological bundle
If I have $u:M\rightarrow D\setminus 0$, $M\subseteq (\mathbb C^2,0)$ compact, $\mathbb C^2 = \mathbb C \times \mathbb C$ and $D$ the Poincare disk, $u$ is holomorphic, surjective, proper and every ...
- 117