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genas
genas
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We have that every holomorphic $\mathbb{CP}^1$-bundle on a compact Riemann surface admits a holomorphic section, due Tsen and as found in Compact Compact Surfaces of Barth, Peters and Van de Ven, for example.

If I add to this bundle a meromorphic flat connection (equivalently a foliation $\mathcal{F}$ which is transversetransversal to the fibers except in finitely many fibers) is it possible to find a transversetransversal section throughto the foliation $\mathcal{F}$?

We have that every holomorphic $\mathbb{CP}^1$-bundle on a compact Riemann surface admits a holomorphic section, due Tsen and as found in Compact Compact Surfaces of Barth, Peters and Van de Ven, for example.

If I add to this bundle a meromorphic flat connection (equivalently a foliation $\mathcal{F}$ which is transverse to the fibers except in finitely many fibers) is it possible to find a transverse section through the foliation $\mathcal{F}$?

We have that every holomorphic $\mathbb{CP}^1$-bundle on a compact Riemann surface admits a holomorphic section, due Tsen and as found in Compact Compact Surfaces of Barth, Peters and Van de Ven, for example.

If I add to this bundle a meromorphic flat connection (equivalently a foliation $\mathcal{F}$ which is transversal to the fibers except in finitely many fibers) is it possible to find a transversal section to the foliation $\mathcal{F}$?

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genas
genas
  • 51
  • 2

We have that every holomorphic $\mathbb{CP}^1$-bundle on a compact Riemann surface admits a holomorphic section, due Tsen and as found in Compact Compact Surfaces of Barth, Peters and Van de Ven, for example.

If I add to this bundle a meromorphic flat connection (equivalently a foliation $\mathcal{F}$ which is transverse to the fibers except in finitely many fibers) is it possible to find a transverse section through the foliation $\mathcal{F}$?

We have that every holomorphic $\mathbb{CP}^1$-bundle on a compact Riemann surface admits a holomorphic section, as found in Compact Compact Surfaces of Barth, Peters and Van de Ven, for example.

If I add to this bundle a meromorphic flat connection (equivalently a foliation $\mathcal{F}$ which is transverse to the fibers except in finitely many fibers) is it possible to find a transverse section through the foliation $\mathcal{F}$?

We have that every holomorphic $\mathbb{CP}^1$-bundle on a compact Riemann surface admits a holomorphic section, due Tsen and as found in Compact Compact Surfaces of Barth, Peters and Van de Ven, for example.

If I add to this bundle a meromorphic flat connection (equivalently a foliation $\mathcal{F}$ which is transverse to the fibers except in finitely many fibers) is it possible to find a transverse section through the foliation $\mathcal{F}$?

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genas
genas
  • 51
  • 2

Existence transverse sections in $\mathbb{CP}^1$-bundles over compact Riemann surfaces

We have that every holomorphic $\mathbb{CP}^1$-bundle on a compact Riemann surface admits a holomorphic section, as found in Compact Compact Surfaces of Barth, Peters and Van de Ven, for example.

If I add to this bundle a meromorphic flat connection (equivalently a foliation $\mathcal{F}$ which is transverse to the fibers except in finitely many fibers) is it possible to find a transverse section through the foliation $\mathcal{F}$?