Abstract
A number of problems concerning an analytic real hypersurface in complex space have been treated by means of its complexification. This manifests itself as a family of complex hypersurfaces, one attached to each point of space. This association of a complex variety to a point is the Segre polar correspondence. Originally B. Segre and E. Cartan used it to attach differential invariants to a nondegenerate real hypersurface. More recently, it has been used in establishing boundary regularity, holomorphic continuation, as well as algebraicity of holomorphic mappings. It also plays a key role in several biholomorphic classification problems. In this paper we shall give a more complete version of the Segre polar correspondence for algebraic real hypersurfaces, in order to treat the phenomenon of double valued reflection.
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References
L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math, de France 109 (1981), 427–474.
J. K. Moser and S. M. Webster, Normal forms for real surfaces in C 2 near complex tangents and hyperbolic surface transformations. Acta Math. 150 (1983), 255–296.
S. M. Webster, On the mapping problem for algebraic real hyper surfaces, Invent. Math. 43 (1977), 53–68.
S. M. Webster, Some birational invariants for algebraic real hypersurfaces, Duke Math. Jour. 45 (1978), 39–46.
S. M. Webster, On the reflection principle in several complex variables, Proc. AMS 71 (1978), 26–28.
S. M. Webster, Double valued reflection in the complex plane, l’Enseign. Math. 42 (1996), 25–48.
S. M. Webster, A note on extremal discs and double valued reflection, AMS Contemp. Math. 205 (1997), 271–276.
S. M. Webster, Real ellipsoids and double valued reflection in complex space, Amer. Jour. Math. 120 (1998), 757–809.
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© 1999 Birkhäuser Boston
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Webster, S.M. (1999). Segre Polar Correspondence and Double Valued Reflection for General Ellipsoids. In: Komatsu, G., Kuranishi, M. (eds) Analysis and Geometry in Several Complex Variables. Trends in Mathematics. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2166-1_13
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DOI: https://doi.org/10.1007/978-1-4612-2166-1_13
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7441-4
Online ISBN: 978-1-4612-2166-1
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