A note on the ampleness of numerically positive log canonical and anti-log canonical divisors

Abstract

In this short note, we consider the conjecture that the log canonical divisor (resp. the anti-log canonical divisor) $K_X+\Delta$ (resp. $-(K_X+\Delta )$) on a pair $(X,\Delta )$ consisting of a complex projective manifold $X$ and a reduced simply normal crossing divisor $\Delta$ on $X$ is ample if it is numerically positive. More precisely, we prove the conjecture for $K_X+\Delta$ with $\Delta \ne 0$ in dimension 4 and for $-(K_X+\Delta )$ with $\Delta \ne 0$ in dimension 3 or 4.

5 pages, LaTeX2e, the former title ``A note on log canonical divisors" changed

References in corpus (1)

• A correction to the paper "Log Abundance Theorem for Threefolds"