Chern-Moser operators and weighted jet determination problems in higher codimension

TL;DR

This paper extends the Chern-Moser approach to higher codimension real submanifolds in complex space, establishing 2-jet determination results for their automorphism groups, especially confirming the theorem in codimension 2.

Contribution

It generalizes the Chern-Moser theorem to higher codimension cases and provides new insights into jet determination for automorphisms.

Findings

Counterexamples for codimension > 2

2-jet determination holds in codimension 2

Extension of Chern-Moser techniques to higher codimension

Abstract

Counterexamples to the 2-jet determination Chern-Moser Theorem in codimension d>2 have recently been constructed. We extend the Chern-Moser approach for hypersurfaces to real submanifolds of higher codimension in complex space to derive results on jet determination for their automorphism group. Using these techniques, we show that the 2-jet determination Chern-Moser Theorem holds in codimension 2.