The horizontal base locus of multiples of tautological sheaves of projectivised cotangent bundles (Q1190209)

Let \(X\) be a smooth complex algebraic surface of general type. The Green- Griffiths conjecture says that the image of any nontrivial holomorphic map from the affine line into \(X\) lies in a fixed proper subvariety. It is proven here for \(X\) a minimal surface with \(c^ 2_ 1>2c_ 2\) (and for \(c^ 2_ 1=2c_ 2\) if \(K_ S\) is ample). For the proof a condition under which the conjecture holds is formulated, in which a real number \(t_ 0\) occurs that is defined in the first part of the paper for any smooth projective variety \(X\): Let \(L\) be the tautological line bundle on the projectivised cotangent bundle of \(X\), then \(t_ 0\) is defined from the base (=fixed) components of multiples of \(L\) that lie over the whole \(X\).