## Base Point Free Theorem of Reid-Fukuda Type

J. Math. Sci. Univ. Tokyo
Vol. 7 (2000), No. 1, Page 1--5.

Fujino, Osamu
Base Point Free Theorem of Reid-Fukuda Type
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Abstract:
Let $(X,Î)$ be a proper dlt pair and $L$ a nef Cartier divisor such that $aL-(K_X+Î)$ is nef and log big on $(X,Î)$ for some $a\in {\Bbb Z}_{>0}$. Then $|mL|$ is base point free for every $m\gg 0$. Furthermore, we give a partial answer to the four-dimensional log abundance conjecture in the appendix.

Mathematics Subject Classification (1991): Primary 14C20; Secondary 14J10
Mathematical Reviews Number: MR1749977

Received: 1999-04-01