| 概要 | We prove that the anti-canonical divisors of weak
Fano 3-folds with log canonical singularities are semiample. Moreover,
we consider semiampleness of the anti-log canonical divisor of
any weak log Fano pair with log canonical singularities. We show
semiampleness dose not hold in general by constructing several
examples. Based on those examples, we propose sufficient conditions
which seem to be the best possible and we prove semiampleness under
such conditions. In particular we derive semiampleness of the
anti-canonical divisors of log canonical weak Fano 4-folds whose
lc centers are at most 1-dimensional. We also investigate the
Kleiman-Mori cones of weak log Fano pairs with log canonical singularities. |