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arXiv · 2010.10220

Construction of counterexamples to the $2-$jet determination Chern-Moser Theorem in higher codimension

Jan Gregorovič·Francine Meylan
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Abstract

We first construct a counterexample of a generic quadratic submanifold of codimension $5$ in $\Bbb C^9$ which admits a real analytic infinitesimal CR automorphism with homogeneous polynomial coefficients of degree $4.$ This example also resolves a question in the Tanaka prolongation theory that was open for more than 50 years. Then we give sufficient conditions to generate more counterexamples to the $2-$jet determination Chern-Moser Theorem in higher codimension. In particular, we construct examples of generic quadratic submanifolds with jet determination of arbitrarily high order.

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Jan Gregorovič, Francine Meylan. 2020-10-20. Construction of counterexamples to the $2-$jet determination Chern-Moser Theorem in higher codimension. https://doi.org/10.4310/mrl.2022.v29.n2.a4

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