Test configurations, large deviations and geodesic rays on toric varieties
Test configurations, large deviations and geodesic rays on toric varieties
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复曲面品种的测试配置、大偏差和测地线
DOI：
10.1016/j.aim.2011.12.025
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发表时间：
2007
影响因子：
1.7
通讯作者：
S. Zelditch
中科院分区：
文献类型：
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作者：
Jian Song;S. Zelditch
本文详细地研究了由Phong和Sturm定义的测地线ϕt的环状变化，对应于Donaldson意义下的测试组态T。我们证明了Phong和Sturm的‘Bergman近似’ϕk(t，z)在C1中收敛到测地线ϕt，并且测地线本身就是C1.1，且也好不到哪里去。特别地，与位势测地线有关的Kähler度量ωt=ω0+I∂∂‘ϕt在某些超曲面上是不连续的，并且在某些开集上是退化的。分析中的一个新奇之处是伯格曼度量、伯格曼核和大偏差理论之间的联系。我们在环面簇的多面体上构造了一系列度量μkz，证明了它们满足大偏差原理，并将速率函数与测地线联系起来。
This article contains a detailed study in the case of a toric variety of the geodesic rays ϕtdefined by Phong and Sturm corresponding to test configurations T in the sense of Donaldson. We show that the ‘Bergman approximations’ ϕk(t,z) of Phong and Sturm converge in C1to the geodesic ray ϕt, and that the geodesic ray itself is C1,1and no better. In particular, the Kähler metrics ωt=ω0+i∂∂¯ϕtassociated to the geodesic ray of potentials are discontinuous across certain hypersurfaces and are degenerate on certain open sets. A novelty in the analysis is the connection between Bergman metrics, Bergman kernels and the theory of large deviations. We construct a sequence of measures μkzon the polytope of the toric variety, show that they satisfy a large deviations principle, and relate the rate function to the geodesic ray.
可积本征函数的分布定律
DOI：
--
发表时间：
2005
期刊：
Annales de l'Institut Fourier 54 no5(予定)
影响因子：
--
作者：
B.Shiffman;T.Tate;S.Zelditch
通讯作者：
S.Zelditch