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Licensed Unlicensed Requires Authentication Published by De Gruyter June 30, 2011

On weak Fano varieties with log canonical singularities

Yoshinori Gongyo EMAIL logo


We prove that the anti-canonical divisors of weak Fano 3-folds with log canonical singularities are semi-ample. Moreover, we consider semi-ampleness of the anti-log canonical divisor of any weak log Fano pair with log canonical singularities. We show semi-ampleness 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 semi-ampleness under such conditions. In particular we derive semi-ampleness of the anti-canonical divisors of log canonical weak Fano varieties whose lc centers are at most 1-dimensional. We also investigate the Kleiman–Mori cones of weak log Fano pairs with log canonical singularities.

Received: 2010-06-15
Published Online: 2011-06-30
Published in Print: 2012-04

©[2012] by Walter de Gruyter Berlin Boston

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