Degeneracy of entire curves into higher dimensional complex manifolds
نویسنده
چکیده
Pursuing McQuillan’s philosophy in proving the Green-Griffiths conjecture for certain surfaces of general type, we deal with the algebraic degeneracy of entire curves tangent to holomorphic foliations by curves. Inspired by the recent work [PS14], we study the intersection of Ahlfors current T [f ] with tangent bundle TF of F , and derive some consequences. In particular, we introduce the definition of weakly reduced singularities for foliations by curves, which requires less work than the exact classification for foliations. Finally we discuss the strategy to prove the Green-Griffiths conjecture for complex surfaces.
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