In this paper, we develop a theory of pseudo-effective sheaves on normal projective varieties. As an application, by running the minimal model program, we show that projective klt varieties with pseudo-effective tangent sheaf can be decomposed into Fano varieties and Q-abelian varieties.

Comment: completely revised version, 13 pages

• 14E30 - Minimal model program (Mori theory, extremal rays)
• 32J25 - Transcendental methods of algebraic geometry (complex-analytic aspects)
• 53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)

• 1 zbMATH Open