2012
DOI: 10.4310/pamq.2012.v8.n3.a4
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On a Family of Hypersurfaces in C2 with Stability Groups Determined by High Jet-Order

Abstract: In this paper, we study the collection of all real-analytic hypersurfaces in C 2 of the form M = (z, w) : Im w = Re w θ(|z| 2 ) . We compute all local automorphisms for such hypersurfaces, providing new examples of hypersurfaces with stability groups determined by arbitrary jet-orders. Moreover, we show that for such hypersurfaces, if the stability group is not determined by 1-jets, then the hypersurface is "generically" spherical. That is, such hypersurfaces are locally spherical at every point except those a… Show more

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