Envelopes of positive metrics with prescribed singularities
Envelopes of positive metrics with prescribed singularities
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DOI：
10.17863/cam.1730
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发表时间：
2012-10
期刊：
影响因子：
--
通讯作者：
J. Ross;D. Nystrom
中科院分区：
文献类型：
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作者：
J. Ross;D. Nystrom
我们研究了具有给定奇异型的正度量包络。首先，我们将Berman的工作推广到这种情况，证明了这种包络的C^{1,1}正则性，表明它们的蒙日-安培测度在一定的“平衡集”上得到支持，并与来自乘子理想的部分Bergman函数的渐近性相联系。我们研究了这些包络在某些产物上的行为，以及它们与K\ ahler势空间中测地线射线中奇异型测试曲线的Legendre变换的关系。最后，我们考虑这些平衡集的相关耗尽函数，将其与Legendre变换和Okounkov体的几何形状联系起来。
We investigate envelopes of positive metrics with a prescribed singularity type. First we generalise work of Berman to this setting, proving C^{1,1} regularity of such envelopes, showing their Monge-Ampere measure is supported on a certain "equilibrium set" and connecting with the asymptotics of the partial Bergman functions coming from multiplier ideals. We investigate how these envelopes behave on certain products, and how they relate to the Legendre transform of a test curve of singularity types in the context of geodesic rays in the space of K\"ahler potentials. Finally we consider the associated exhaustion function of these equilibrium sets, connecting it both to the Legendre transform and to the geometry of the Okounkov body.