On the Catlin Multitype of Sums of Squares Domains

Abstract

For a sum of squares domain of finite D’Angelo 1-type at the origin, we show that the polynomial model obtained from the computation of the Catlin multitype at the origin of such a domain is likewise a sum of squares domain. We also prove, under the same finite type assumption that the multitype is an invariant of the ideal of holomorphic functions defining the domain. Both results are proven using Martin Kolář’s algorithm for the computation of the multitype introduced in Kolář (Int Math Res Not (IMRN) 18:3530–3548, 2010). Given a sum of squares domain, we rewrite the Kolář algorithm in terms of ideals of holomorphic functions and also introduce an approach that explicitly constructs the homogeneous polynomial transformations used in the algorithm.