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

2003/05/31 by Shigetaka Fukuda
Mathematics · #math.AG #msc:14E30

paper · pdf

published as Tokyo J. Math. 27 (2004), no. 2, 377--380 · 5 pages, LaTeX2e, the former title ``A note on log canonical divisors" changed

arxiv created 2003/09/02 · arxiv updated 2009/11/30

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≠ 0 in dimension 4 and for -(K_X + Δ) with Δ≠ 0 in dimension 3 or 4.

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