Rationally connected foliations on surfaces

Mathematics – Algebraic Geometry

Scientific paper

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8 pages

Scientific paper

In this short note we study foliations with rationally connected leaves on
surfaces. Our main result is that on surfaces there exists a polarisation such
that the Harder-Narasimhan filtration of the tangent bundle with respect to
this polarisation yields the maximal rationally quotient of the surface.

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