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Ali Taghavi
Ali Taghavi
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Is there a singular holomorphic foliation $F$ of $\mathbb{C}P^2$ which does not admit a global transverse holomorphic curve.? More precisely there is no an immersed holomorphic submanifold of $\mathbb{C}P^2$ which intersect all regular leaves, transversely? If there exist such an example $F$, does this foliation admit a smooth(but not necessarily holomorphic) global transverse submanifold (of real dimension 2)?

Is there a singular holomorphic foliation $F$ of $\mathbb{C}P^2$ which does not admit a global transverse holomorphic curve. More precisely there is no an immersed holomorphic submanifold of $\mathbb{C}P^2$ which intersect all regular leaves, transversely? If there exist such an example $F$, does this foliation admit a smooth(but not necessarily holomorphic) global transverse submanifold (of real dimension 2)?

Is there a singular holomorphic foliation $F$ of $\mathbb{C}P^2$ which does not admit a global transverse holomorphic curve? More precisely there is no an immersed holomorphic submanifold of $\mathbb{C}P^2$ which intersect all regular leaves, transversely? If there exist such an example $F$, does this foliation admit a smooth(but not necessarily holomorphic) global transverse submanifold (of real dimension 2)?

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Source Link
Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

Is there a singular holomorphic foliation $F$ of $\mathbb{C}P^2$ which does not admit a global transverse holomorphic curve. More precisely there is no an immersed holomorphic submanifold of $\mathbb{C}P^2$ which intersect all regular leaves, transversely? If there exist such an example $F$, does this foliation admit a smooth(but not necessarily holomorphic) global transverse submanifold (of real dimension 2)?

Is there a singular holomorphic foliation $F$ of $\mathbb{C}P^2$ which does not admit a global transverse holomorphic curve. More precisely there is no an immersed holomorphic submanifold of $\mathbb{C}P^2$ which intersect all regular leaves, transversely? If there exist such an example $F$, does this foliation admit a smooth global transverse submanifold (of real dimension 2)?

Is there a singular holomorphic foliation $F$ of $\mathbb{C}P^2$ which does not admit a global transverse holomorphic curve. More precisely there is no an immersed holomorphic submanifold of $\mathbb{C}P^2$ which intersect all regular leaves, transversely? If there exist such an example $F$, does this foliation admit a smooth(but not necessarily holomorphic) global transverse submanifold (of real dimension 2)?

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Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

A Singular Foliation of $\mathbb{C}P^2$ which does not admit a global transverse submanifold

Is there a singular holomorphic foliation $F$ of $\mathbb{C}P^2$ which does not admit a global transverse holomorphic curve. More precisely there is no an immersed holomorphic submanifold of $\mathbb{C}P^2$ which intersect all regular leaves, transversely? If there exist such an example $F$, does this foliation admit a smooth global transverse submanifold (of real dimension 2)?