4,143 research outputs found
Triangular resolutions and effectiveness for holomorphic subelliptic multipliers
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 , where is
constructed from pre-multipliers and 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
- …