Questions tagged [holomorphic-foliations]

For question concerning foliation theory in the holomorphic case: germs of foliation singularities, holomorphic foliations on complex manifolds, Pfaff fields, etc.

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Show that a generic line is not a leaf of an algebraic foliation of $\mathbb P^2$

Consider a foliation of $\mathbb P^2$, whose leaves in the affine part $z = 1$ are the integral curves of a polynomial vector field $$X = P \frac \partial {\partial x} + Q \frac \partial {\partial y}$...
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What are the prerequisites to learning about Lie groupoids, Lie algebroids and holomorphic foliations?

I am a graduate student of Theoretical Physics and intend to take a course titled "Introduction to Lie groupoids, Lie algebroids and holomorphic foliations". The course page doesn't have information ...
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Conormal and Tangent Sheaves of a Distribuition in $\mathbb{P}^{n}$ when $n = 2$ and $n = 3$

Definition 1): A codimension one distribution of degree $d \geq 0$ in $\mathbb{P}^{n}$ is given by an exact sequence: $$\mathscr{F}: 0 \longrightarrow T_{\mathscr{F}} \longrightarrow T\mathbb{P}^{n}\...
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177 views

Exact sequence on $\mathbb{P}^3$ obtained from Euler sequence

In the article of title: On the singular scheme of codimension one holomorphic foliations in $\mathbb{P}^3$ the author states that the sequence on $\mathbb{P}^3$ $$0\longrightarrow \mathcal{F}\oplus\...
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167 views

Isomorphisms of complex (foliated) n-tori

From here: https://www.encyclopediaofmath.org/index.php/Complex_torus A complex torus is a complex Abelian Lie group obtained from the $n$-dimensional complex space $\mathbb{C}^n$ by factorizing ...
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348 views

holomorphic vector fields tangent to a hypersurface

Let $(V,0)\subset (\mathbb{C}^n,0)$, $n\geq 3$ a (germ of) hypersurface given by $\{f=0\}$, $f$ holomorphic. A (germ of) holomorphic vector field $X$ leaves $V$ invariant if ${\rm d}f(X)$ belongs to ...