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

On weak Fano varieties with log canonical singularities

Yoshinori Gongyo EMAIL logo

Abstract

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

Downloaded on 29.11.2022 from frontend.live.degruyter.dgbricks.com/document/doi/10.1515/CRELLE.2011.111/html
Scroll Up Arrow