学术报告（Masataka Iwai 2024.5.16）

Abstract: It has been shown by Miyaoka that, for a minimal projective variety X with at most klt singularities  (i.e. the canonical divisor Kx is nef), the Miyaoka's inequality: 3c_2(X)H^{n-2} \ge c_1(X)^2H^{n-2}  holds for any ample divisor H. In this talk, I will present that if the equality holds in Miyaoka's inequality, then $K_X$ is  semiample. Moreover, I will talk about the structure of X in this case. If time permits, I will also introduce the structure of a minimal projective klt variety X with a  nef anti-canonical divisor with c_2(T_X)H^{n-2}=0. This is a joint work with Shin-ichi Matsumura (Tohoku University) and Niklas Muller (Essen  University). (arXiv:2404.07568)