Coherence and other properties of sheaves in the Kohn algorithm
In this paper, techniques by \textit{J.-C. Tougeron} [C. R. Acad. Sci., Paris 260, 2971--2973 (1965; Zbl 0131.20603)] are used to show the following result: let \(\Omega \subset \mathbb C^n\) be a domain with real-analytic boundary \(b\Omega,\) let \(\tilde U\) be any open subset of \(b\Omega\) such that \(\tilde U\) is contained in a compact semianalytic subset \(Y\) of \(b\Omega;\) then the ideal sheaf \(\tilde \mathcal I^q\) of real-analytic subelliptic multipliers for the \(\overline \partial\)-Neumann problem on \((p,q)\) forms defined on \(\tilde U\) is coherent; additionally, if \(\Omega\) is pseudoconvex, the multiplier ideal sheaf \(\tilde \mathcal I^q_k\) given by the modified Kohn algorithm on \(\tilde U\) at step \(k\) for each \(k\geq 1\) is also coherent; if \(\Omega\) is bounded, \(b\Omega\) itself may be taken as \(\tilde U.\) It is shown that this implies a much stronger result than Kohn's original method in the real-analytic case for a domain of finite D'Angelo type [\textit{J. J. Kohn}, Acta Math. 142, 79--122 (1979; Zbl 0395.35069)].
scientific article; zbMATH DE number 6359570