Abstract
The purpose of this paper is to study the structure of the sets of tangent vectors and tangent planes to a complex analytic variety, particularly in the neighborhood of singular points of the variety. We prove the existence of a stratification of the variety which has nice properties relative to tangent planes. Corresponding properties of real analytic varieties (which are the real parts of of complex ones) may be found by considering the corresponding complex analytic variety.
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References
S. S. Abhyankar, Local Analytic Geometry, Academic Press, New York, 1964.
E. Bishop, Partially analytic spaces, Amer. J. Math., 83 (1961), 669 - 692.
H. CARTAN, Séminaire 1951–52, Ecole Normal Sup., Paris.
H. Grauert and R. Remmert, Zur Theorie der Modifikationen: I. Stetige und eigentliche Modifikationen komplexer Räume., Math. Ann., 129 (1955), 274 - 296.
H. Grauert and R. Remmert, Komplexe Räume, Math. Ann., 136 (1958), 245–318.
M. Herve, Several Complex Variables, Local Theory, Oxford University Press, London, 1963.
E. Kreyszig, Stetige Modifikationen komplexer Mannigfaltigkeiten, Math. Ann., 128 (1955), 479–492.
R. Remmert, Holomorphe und meromorphe Abbildungen komplexer Räume, Math. Ann., 133 (1957), 328–370.
R. Remmert and K. Stein, Über die wesentlichen Singularitäten analytischer Mengen, Math. Ann., 126 (1953), 263–306.
H. Rossi, Analytic spaces with compact subvarieties, Math. Ann., 146 (1962), 129–145.
H. Whitney, “Local properties of analytic varieties”, Differential and Combinatorial Topology, Princeton University Press, 1965.
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© 1992 Birkhäuser Boston
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Whitney, H. (1992). Tangents to an Analytic Variety. In: Eells, J., Toledo, D. (eds) Hassler Whitney Collected Papers. Contemporary Mathematicians. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2972-8_34
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DOI: https://doi.org/10.1007/978-1-4612-2972-8_34
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7740-8
Online ISBN: 978-1-4612-2972-8
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