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

Shigetaka Fukuda
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Abstract

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

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Shigetaka Fukuda. 2003-09-02. A note on the ampleness of numerically positive log canonical and anti-log canonical divisors. https://arxiv.org/abs/math/0305357

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