On weak Fano varieties with log canonical singularities
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Yoshinori Gongyo
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.
©[2012] by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Extended rotation algebras: Adjoining spectral projections to rotation algebras
- Hochschild and cyclic homology of Yang–Mills algebras
- Rational curves on hypersurfaces
- Strong rational connectedness of surfaces
- Concentration theorem and relative fixed point formula of Lefschetz type in Arakelov geometry
- On weak Fano varieties with log canonical singularities
Articles in the same Issue
- Extended rotation algebras: Adjoining spectral projections to rotation algebras
- Hochschild and cyclic homology of Yang–Mills algebras
- Rational curves on hypersurfaces
- Strong rational connectedness of surfaces
- Concentration theorem and relative fixed point formula of Lefschetz type in Arakelov geometry
- On weak Fano varieties with log canonical singularities
