Invariants of Varieties and Singularities inspired by Kahler-Einstein problems
Invariants of Varieties and Singularities inspired by Kahler-Einstein problems
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DOI：
10.3792/pjaa.91.50
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发表时间：
2014-11
期刊：
影响因子：
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通讯作者：
Y. Odaka
中科院分区：
文献类型：
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作者：
Y. Odaka
我们将k -稳定性（Tian, Donaldson）的框架扩展到更一般的代数-几何设置，例如（固定）奇点的部分去象形化，高维基上的（不一定是平坦的）族和经典的双几何曲面。我们还观察到，在我们的广义设置中，体积函数的“凹性”意味着（广义的）Donaldson-Futaki不变量沿着最小模型程序减小。本文还证明了与MMP理论相联系的几个相关结果，其中一些结果甚至是在曲线上族的原始背景下的新结果。
We extend the framework of K-stability (Tian, Donaldson) to more general algebro-geometric setting, such as partial desingularisations of (fixed) singularities, (not necessarily flat) families over higher dimensional base and the classical birational geometry of surfaces. We also observe that "concavity" of the volume function implies decrease of the (generalised) Donaldson-Futaki invariants along the Minimal Model Program, in our generalised settings. Several related results on the connection with the MMP theory, some of which are new even in the original setting of families over curves, are also proved.