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

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

2003-05-26

arxiv.org/abs/math/0305357v3

Tokyo J. Math. 27 (2004), no. 2, 377--380

Mathematics

Algebraic Geometry

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

Scientific paper

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 $\Delta \neq 0$ in dimension 4 and for $-(K_X + \Delta)$ with $\Delta \neq 0$ in dimension 3 or 4.

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