Note on characterizations of projective spaces
  We prove a numerical characterization of $\mathbb{P}^n$ for varieties with at worst isolated local complete intersection quotient singularities. In dimension three, we prove such a numerical characterization of $\mathbb{P}^3$ for normal $\mathbb{Q}$-Gorenstein projective varieties. 
Jiun-Cheng Chen, Hsian-Hua Tseng