Note on characterizations of projective spaces

Jiun-Cheng Chen, Hsian-Hua Tseng

Published 2005-09-28, updated 2006-03-15Version 2

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.