Semiampleness theorem for weak log Fano varieties

I. V. Karzhemanov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The semiampleness of the divisor $-(K_X+S)$ is proved for a pair $(X,S)$ with purely log terminal $\mathbb Q$-factorial singularities, where $X$ is a three-dimensional normal projective algebraic variety and $S\subset X$ is a normal surface such that the divisor $-(K_X+S)$ is nef and big.
Bibliography: 8 titles.

UDC: 512.763

MSC: Primary 14E30; Secondary 14E05, 14G30

Received: 17.08.2005

DOI: 10.4213/sm1134

 English version: Sbornik: Mathematics, 2006, 197:10, 1459–1465

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