An application of a $C^2$-estimate for a complex Monge-Amp\`ere equation

Abstract

By studying a complex Monge-Amp\`ere equation, we present an alternate proof to a recent result of Chu-Lee-Tam concerning the projectivity of a compact K\"ahler manifold $N^n$ with $\Ric_k< 0$ for some integer $k$ with $1<k<n$, and the ampleness of the canonical line bundle $K_N$.