全纯次椭圆乘子的三角分解和有效性
Triangular resolutions and effectiveness for holomorphic subelliptic multipliers
摘要：
一个解决方案的有效性问题，在科恩的算法产生次椭圆乘子提供的域，包括那些由平方和的全纯函数（也包括无限和）。这些领域是特别感兴趣的，由于它们与复杂和代数几何的关系，特别是，似乎包括所有以前已知的情况。结合M. Fassina，我们的有效性方法允许建立更一般的域类的有效的次椭圆估计。我们的主要新工具，三角形的决议，是建设的亚椭圆乘子分解为$Q\circΓ$，其中$Γ$是由前乘子和$Q$是一个三角形系统的一部分。的有效性证明了通过一系列新提出的程序，这里称为元程序，建立在顶部的Kohn的程序，其中的顺序subellipticity可以有效地跟踪。重要的灵感来源是代数几何技术的Y。T. Siu和D.W.凯特林和J·P·丹杰洛所提出的程序是纯代数的，因此也可以感兴趣的几何和计算问题，涉及雅可比行列式，如解决奇点的全纯映射。
英文摘要：
A solution to the effectiveness problem in Kohn's algorithm for generating subelliptic multipliers is provided for domains that include those given by sums of squares of holomorphic functions (also including infinite sums). These domains are of particular interest due to their relation with complex and algebraic geometry and in particular, seem to include all previously known cases. Furthermore, combined with a recent result of M. Fassina, our effectiveness method allows establishing effective subelliptic estimates for more general classes of domains. Our main new tool, a triangular resolution, is the construction of subelliptic multipliers decomposable as $Q\circΓ$, where $Γ$ is constructed from pre-multipliers and $Q$ is part of a triangular system. The effectiveness is proved via a sequence of newly proposed procedures, called here meta-procedures, built on top of the Kohn's procedures, where the order of subellipticity can be effectively tracked. Important sources of inspiration are algebraic-geometric techniques by Y.-T. Siu and procedures for triangular systems by D.W. Catlin and J.P. D'Angelo. The proposed procedures are purely algebraic and as such can also be of interest for geometric and computational problems involving Jacobian determinants, such as resolving singularities of holomorphic maps.
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