Algebraic estimates, stability of local zeta functions, and uniform estimates for distribution functions
Algebraic estimates, stability of local zeta functions, and uniform estimates for distribution functions
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DOI：
10.2307/2661384
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发表时间：
2000-07
影响因子：
4.9
通讯作者：
Duong H. Phong;J. Sturm
中科院分区：
文献类型：
--
作者：
Duong H. Phong;J. Sturm
提出了一种“代数估计法”，并用于研究函数f在小变形下积分R B jf（z）j i-dV的稳定性.这些估计用代数簇的函数空间fR（z）= jP（z）j“=jQ（z）j-g的分层来描述，在每个代数簇上，R（z）的积分的大小由显式代数表达式给出。该方法给出了一个关于Tian在二维空间稳定性的结果的独立证明，并将该结果部分推广到三维空间。在任意维数下，结合Siu的一个关键引理，它建立了映射c的连续性！R B jf（z;c）ji-dV 1 dVn当f（z;c）是（z;c）的全纯函数.特别是导极点在f中是不连续的，这也加强了Lichtin的一个较早的结果。
A method of \algebraic estimates" is developed, and used to study the stability properties of integrals of the form R B jf(z)j i‐ dV , under small deformations of the function f. The estimates are described in terms of a stratiflcation of the space of functionsfR(z )= jP (z)j " =jQ(z)j ‐ g by algebraic varieties, on each of which the size of the integral of R(z) is given by an explicit algebraic expression. The method gives an independent proof of a result on stability of Tian in 2 dimensions, as well as a partial extension of this result to 3 dimensions. In arbitrary dimensions, combined with a key lemma of Siu, it establishes the continuity of the mapping c! R B jf(z;c)j i‐ dV1¢¢¢dVn when f(z;c) is a holomorphic function of (z;c). In particular the leading pole is semicontinuous in f, strengthening also an earlier result of Lichtin.