Coherence and Other Properties of Sheaves in the Kohn Algorithm

TL;DR

This paper proves quasi-flasqueness of sheaves of subelliptic multipliers in the Kohn algorithm for pseudoconvex domains, using advanced techniques to improve previous results and analyze properties in real-analytic settings.

Contribution

It establishes quasi-flasqueness and quasi-coherence of sheaves associated with the Kohn algorithm, refining earlier work by Kohn with new techniques for real-analytic domains.

Findings

Proves quasi-flasqueness of sheaves in the smooth case.

Shows quasi-coherence for real-analytic defining functions.

Sharpens Kohn's 1979 results using Tougeron's techniques.

Abstract

In the smooth case, we prove quasi-flasqueness for the sheaves of all subelliptic multipliers as well as at each of the steps of the Kohn algorithm on a pseudoconvex domain in $\C^n.$ We use techniques by Jean-Claude Tougeron to show that if the domain has a real-analytic defining function, the modified Kohn algorithm involving generating ideals and taking real radicals only in the ring of real-analytic germs yields quasi-coherent sheaves. This sharpens a result obtained by J. J. Kohn in 1979.