Triangular resolutions and effectiveness for holomorphic subelliptic multipliers

A solution to the effectiveness problem in Kohn's algorithm for generating holomorphic subelliptic multipliers is provided general classes of domains finite type C n , that include so-called special given by and infinite sums squares absolute values functions. Also included a more class recently discovered M. Fassina [23] . More generally, any smoothly bounded pseudoconvex domain we introduce an invariantly defined associated sheaf S -subalgebras function germs, combined with result Fassina, reduces existence effective estimates at p purely algebraic geometric question controlling multiplicity Our main new tool, triangular resolution construction decomposable as Q ∘ Γ where constructed from pre-multipliers part system. The proved via sequence newly proposed procedures, called here meta-procedures built on top order subellipticity can be effectively tracked. Important sources inspiration are techniques Y.-T. Siu [54] [55] procedures systems D.W. Catlin J.P. D'Angelo [16] [8] such wider interest computational problems involving Jacobian determinants, resolving singularities maps.