论文标题
三角形分辨率和对全态亚细倍数的有效性
Triangular resolutions and effectiveness for holomorphic subelliptic multipliers
论文作者
论文摘要
为KOHN算法中的有效性问题解决了产生下层状乘数的解决方案，该域提供了域，其中包括由全体形函数的正方形（还包括无限总和）给出的域。这些域特别引起了人们的关注，因为它们与复杂和代数的几何形状的关系，尤其是包括所有以前已知的案例。此外，加上Fassina M. Fassina的最新结果，我们的有效性方法允许为更多一般类域的有效的下层次估计值。 我们的主要新工具是一种三角形分辨率，是构建亚细乘数可解释为$ q \circγ$，其中$γ$是由pre-multipliers构建的，$ q $是三角系统的一部分。有效性是通过一系列新提出的程序证明的，称为此处称为Meta-Procecedures，这些程序在Kohn的程序之上构建，可以有效地跟踪subellirticity的顺序。灵感的重要来源是Y.-T的代数几何技术。 D.W.的SIU和三角系统的程序Catlin和J.P. D'Angelo。 所提出的程序纯粹是代数，因此对于涉及雅各布决定因素的几何和计算问题，例如解决霍明态图的奇异性。
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.
