Catlin's boundary systems for sums of squares domains

For any given sum of squares domain in Cn, we reduce the complexity in Catlin's multitype techniques by giving a complete normalization of the geometry. Using this normalization result, we present a more elementary proof of the equality of the Catlin multitype and the commutator multitype for such domains when both invariants are finite. Finally, we reformulate algebraically Catlin's machinery for the commutator multitype computation at the origin for any given sum of squares domain in Cn. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Automated summary

In this article, we reduce the complexity in Catlin's multitype techniques for any given sum of squares domain in Cn by providing a complete normalization of the geometry. With this normalization result, we present a simpler proof of the equality between Catlin multitype and commutator multitype for such domains when both invariants are finite. Finally, we reformulate algebraically Catlin's machinery for computing the commutator multitype at the origin for any given sum of squares domain in Cn.