A Bishop surface with a vanishing Bishop invariant

Details A Bishop surface with a vanishing Bishop invariant A Bishop surface with a vanishing Bishop invariant

2007-04-16

arxiv.org/abs/0704.2040v2

Mathematics

Complex Variables

Scientific paper

We derive a complete set of invariants for a formal Bishop surface near a point of complex tangent with a vanishing Bishop invariant under the action of formal transformations. We prove that the modular space of Bishop surfaces with a vanishing Bishop invariant and with a fixed Moser invariant $s<\infty$ is of infinite dimension. We also prove that the equivalence class of the germ of a generic real analytic Bishop surface near a complex tangent with a vanishing Bishop invariant can not be determined by a finite part of the Taylor expansion of its defining equation. This answers, in the negative, a problem raised by J. Moser in 1985 after his joint work with Webster in 1983 and his own work in 1985.

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