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A simple criterion for local hypersurfaces to be algebraic. (English) Zbl 0584.14021
The author gives ”a necessary and sufficient condition for d pieces of hypersurface to be contained in an algebraic hypersurface of degree d”.
Reviewer: U.Vetter

MSC:
14J99 Surfaces and higher-dimensional varieties
14N05 Projective techniques in algebraic geometry
14A05 Relevant commutative algebra
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[1] Sophus Lie, Die Theorie der Translationsflächen und das Abelsche Theorem , Leipziger Berichte (1896), 141-168, Also, Gesammelte Abhandlungen, II, 2, Leipzig: B. G. Teubner, 1937, pp. 526-579.
[2] Georg Scheffers, Das Abel’sche Theorem und das Lie’sche Theorem über Translationsflächen , Acta Mathematica 28 (1904), 65-91. · JFM 35.0426.01
[3] Jay Alan Wood, An algebraization theorem for local hypersurfaces in projective space , Ph.D. Dissertation, University of California, Berkeley, 1982.
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