Minimal projective varieties satisfying Miyaoka's equality

Abstract In this paper, we establish a structure theorem for a minimal projective klt variety satisfying Miyaoka's equality . Specifically, we prove that the canonical divisor is semi‐ample and that the Kodaira dimension is equal to 0, 1, or 2. Furthermore, based on this abundance result, we show that a maximally quasi‐étale cover of is smooth, and we explicitly describe the structure of the Iitaka fibration. In addition, we prove an analogous result for projective klt varieties with numerically effective anti‐canonical divisor.