On weak Fano varieties with log canonical singularities
On weak Fano varieties with log canonical singularities
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DOI：
10.1515/crelle.2011.111
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发表时间：
2009-11
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通讯作者：
Yoshinori Gongyo
中科院分区：
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作者：
Yoshinori Gongyo
摘要证明了具有对数正则奇点的弱Fano 3褶的反正则因子是半样本的。此外，我们还考虑了具有对数正则奇点的任意弱对数Fano对的反对数正则因子的半充裕性。我们通过构造几个例子来证明半丰裕性一般不成立。在这些例子的基础上，我们提出了似乎是最好的充分条件，并在这些条件下证明了半充足性。特别地，我们导出了lc中心不超过一维的对数正则弱Fano变的反正则因子的半丰性。我们还研究了具有对数正则奇点的弱对数Fano对的Kleiman-Mori锥。
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.