Minimal projective varieties satisfying Miyaoka's equality

Abstract

In this paper, we establish a structure theorem for minimal projective klt varieties $X$ that satisfiy Miyaoka's equality $3c_2(X) = c_1(X)^2$. Specifically, we prove that the canonical divisor $K_X$ is semi-ample and that the Kodaira dimension $\kappa(K_X)$ is either $0$, $1$, or $2$. Furthermore, based on this abundance result, we show that a maximally quasi-\'etale cover of $X$ is smooth, and we describe explicitly the structure of the Iitaka fibration. Additionally, we prove a similar result for projective klt varieties with a nef anti-canonical divisor.