Structure theorems for compact Kähler manifolds with nef anticanonical bundles

Abstract

This survey presents various results concerning the geometry of compact Kähler manifolds with numerically effective first Chern class: structure of the Albanesemorphism of such manifolds, relations tying semipositivity of theRicci curvature with rational connectedness, positivity properties of the Harder-Narasimhan filtration of the tangent bundle.