Rational curves on compact Kähler manifolds

Abstract

Mori's theorem yields the existence of rational curves on projective manifolds such that the canonical bundle is not nef. In this paper we study compact Kähler manifolds such that the canonical bundle is pseudoeffective, but not nef. We present an inductive argument for the existence of rational curves that uses neither deformation theory nor reduction to positive characteristic. The main tool for this inductive strategy is a weak subadjunction formula for lc centres associated to certain big cohomology classes.

Jordan property for groups of bimeromorphic automorphisms of compact Kähler threefolds

“…By Theorem 5.2 this would give the Jordan property for Bim(X) in higher dimensions. In [CH20] Cao and Höring made some progress in this direction.…”

Jordan property for groups of bimeromorphic automorphisms of compact Kähler threefolds

“…By Theorem 5.2 this would mean the Jordan property of Bim(X) in higher dimensions. In [29] Cao and Höring made some progress in this direction.…”

On the $4$-dimensional minimal model program for Kähler varieties

“…When dim X = 3, using Boucksom's divisorial Zariski deocomposition [Bou04] it is shown in [HP16,CHP16] (also see [DH20, Lemma 2.6]) that K X + B is nef if and only if (K X + B) • C ≥ 0 for all curves C ⊂ X. This result is expected to be true in dim X ≥ 4, but a proof is not yet known, the proof in dimension 3 does not automatically extend in higher dimensions; for a partial result in higher dimensions see [CH20].…”