Rational curves on compact Kaehler manifolds

Junyan Cao (1) , Andreas Höring (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 LJAD - Laboratoire Jean Alexandre Dieudonné

We present an inductive strategy to show the existence of rational curves on compact Kaehler manifolds which are not minimal models but have a pseudoeffective canonical bundle. The tool for this inductive strategy is a weak subadjunction formula for lc centres associated to certain big cohomology classes. This subadjunction formula is based, as in the projective case, on positivity arguments for relative adjoint classes.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Junyan Cao, Andreas Höring. Rational curves on compact Kaehler manifolds. 2015. ⟨hal-01116093⟩