ON THE ANTI-CANONICAL GEOMETRY OF Q-FANO THREEFOLDS
ON THE ANTI-CANONICAL GEOMETRY OF Q-FANO THREEFOLDS
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发表时间：
2014
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通讯作者：
Meng Chen;Chen Jiang
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作者：
Meng Chen;Chen Jiang
对于Q-Fano三重X，KX是其上的典型因子，我们研究了由线性系统导出的几何|MKX|证明了反m-正则映射'-m在它的象上是双有理的，对所有的m ∈ 39.弱Q-Fano 3-重X是指在最坏的终端奇点上KX是Q-Cartier，nef和big的射影X。对于弱Q-Fano 3-folds，我们证明'-m对于所有m 97都是其像上的双有理。
For a Q-Fano 3-fold X on which KX is a canonical divisor, we investigate the geometry induced from the linear system | mKX| in this paper and prove that the anti-m-canonical map '−m is birational onto its image for all m � 39. By a weak Q-Fano 3-fold X we mean a projective one with at worst terminal singularities on which KX is Q-Cartier, nef and big. For weak Q-Fano 3-folds, we prove that '−m is birational onto its image for all m � 97.