Bounds for log canonical thresholds with applications to birational rigidity
Bounds for log canonical thresholds with applications to birational rigidity
复制标题
对数规范阈值的界限及其在双有理刚度中的应用
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
M. Mustaţă
中科院分区：
文献类型：
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作者：
T. Fernex;L. Ein;M. Mustaţă
我们使用交叉理论、退化技术和喷射方案来研究对数规范阈值。我们的第一个结果通过适当的平滑态射根据图像的对数规范阈值给出了一对的对数规范阈值的下界。这又基于对数规范阈值和塞缪尔多重性之间的不等式，概括了我们之前来自 math.AG/0205171 的结果。然后，我们根据非对数终端轨迹的维数给出由同次齐次方程定义的仿射方案的对数规范阈值的下界（本部分取代 math.AG/0105113）。作为我们结果的应用，我们证明了 P^N 中每个 N 级光滑超曲面的双有理超刚度，如果 4\leq N\leq 12。
We use intersection theory, degeneration techniques and jet schemes to study log canonical thresholds. Our first result gives a lower bound for the log canonical threshold of a pair in terms of the log canonical threshold of the image by a suitable smooth morphism. This in turn is based on an inequality relating the log canonical threshold and the Samuel multiplicity, generalizing our previous result from math.AG/0205171. We then give a lower bound for the log canonical threshold of an affine scheme defined by homogeneous equations of the same degree in terms of the dimension of the non log terminal locus (this part supersedes math.AG/0105113). As an application of our results, we prove the birational superrigidity of every smooth hypersurface of degree N in P^N, if 4\leq N\leq 12.