Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of counterexamples to the $2-$jet determination Chern-Moser
  Theorem in higher codimension   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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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio