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Griffiths, Phillip; Harris, Joseph

Algebraic geometry and local differential geometry. (English) Zbl 0426.14019

Ann. Sci. Éc. Norm. Supér. (4) 12, 355-452 (1979).
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Cited in 21 Reviews
Cited in 78 Documents

MSC:

14J40 \(n\)-folds (\(n>4\))
14J17 Singularities of surfaces or higher-dimensional varieties
14N05 Projective techniques in algebraic geometry
14C20 Divisors, linear systems, invertible sheaves
32Q99 Complex manifolds
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
53B99 Local differential geometry
53A20 Projective differential geometry

Keywords:

local differential geometry; second fundamental form; differential of Gauss mappings; degenerate dual varieties; Chern forms; complex analytic manifold; linear system
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\textit{P. Griffiths} and \textit{J. Harris}, Ann. Sci. Éc. Norm. Supér. (4) 12, 355--452 (1979; Zbl 0426.14019)
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References:

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[2] E. CARTAN , Groupes finis et continus et la géométrie différentielle , Gauthier-Villars, Paris, 1937 . · JFM 63.1227.02
[3] E. CARTAN , Sur la déformation projective des surfaces , œuvres complètes ; Vol. 1, Part 3, 1955 , pp. 441-539, Gauthier-Villars, Paris.
[4] G. FUBINI , and E. CECH , Géométrie projective différentielle des surfaces , Gauthier-Villars, Paris, 1931 . Zbl 0002.35101 | JFM 57.0936.01 · Zbl 0002.35101
[5] W. FULTON and A. HANSEN , A Connectedness Theorem for Projective Varieties, with Applications to Intersections and Singularities of Mappings (preprint available from Brown University). · Zbl 0389.14002
[6] M. GREEN , The Moving Frame, Differential Invariants and Rigidity Theorems for Curves in Homogeneous Spaces (Duke J. Math., Vol. 45, 1978 ). Article | MR 80a:53011 | Zbl 0414.53039 · Zbl 0414.53039
[7] P. GRIFFITHS , On Cartan’s Method of Lie Groups and Moving Frames as Applied to Existence and Uniqueness Questions in Differential Geometry (Duke J. Math., Vol. 41, 1974 , pp. 775-814). Article | MR 53 #14355 | Zbl 0294.53034 · Zbl 0294.53034
[8] P. GRIFFITHS , Hermitian Differential Geometry, Chern Classes, and Positive Vector Bundles, Global Analysis (papers in honor of K. Kodaira), Princeton Press, 1969 , pp. 185-251. MR 41 #2717 | Zbl 0201.24001 · Zbl 0201.24001
[9] P. GRIFFITHS and J. HARRIS , Principles of Algebraic Geometry , John Wiley and Sons, New York, 1978 . MR 80b:14001 | Zbl 0408.14001 · Zbl 0408.14001
[10] G. JENSEN , Higher Order Contact of Submanifolds of Homogeneous Spaces (Lecture Notes in Math., No. 610, Springer-Verlag, New York, 1977 ). MR 58 #18226 | Zbl 0356.53005 · Zbl 0356.53005
[11] T. OCHIAI , On Holomorphic Curves in Algebraic Varieties with Ample Irregularity (Invent. Math., Vol. 43, 1977 , pp. 83-96). MR 57 #12912 | Zbl 0374.32006 · Zbl 0374.32006
[12] B. SMYTHE , Weakly Ample Kähler Manifolds and Euler Number , (Math. Ann., Vol. 224, 1976 , pp. 269-279). Zbl 0354.32009 · Zbl 0354.32009
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