Abstract
In this paper we shall prove two theorems concerning holomorphic mappings of large open sets of ℂk into algebraic varieties. Both are in response to well-known outstanding problems, and we feel that the techniques introduced should in each case have further applications.
Research partially supported by NSF Grant and the Alfred P. Sloan Foundation.
Research partially supported by NSF Grant # MCS7707782.
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References
A. Bloch, Sur les systémes de fonctions uniformes satisfaisant â l’equation d’une variété algébrique dont l’irrégularité dépasse la dimension. J. de Math. V, 19–66 (1926).
F. Bogomolov, Families of curves on a surface of general type. Sov. Math. Dokl. 18, 1294–1297 (1977).
R. Brody, Intrinsic metrics and measures on compact complex manifolds. Ph.D. Thesis, Harvard Univ., 1975.
G. Castelnuovo and F. Enriques, Grundeigenschaften der Algebraischen Flächen. In Encyklop. d. Math. Wissensch., Vol. 3, 1903, pp. 635–768.
M. Cowen, Families of negatively curved Hermitian manifolds. Proc. Amer. Math. Soc. 39 362–366 (1973).
M. Cowen and P. Griffiths, Holomorphic curves and metrics of negative curvature. J. Analyse Math.
P. Deligne and D. Mumford, The irreducibility of the space of curves of a given genus. Publ. Math. IHES 36, 75–109 (1969).
I. Dolgacev, Weighted Projective Varieties, to appear.
R. Donagi, On the geometry of Grassmannians. Duke Math. J. 44, 795–837 (1977).
H. Grauert and H. Reckziegel, Hermitesche Metriken and normale familien holomorpher Abbildungen. Math. Z. 89, 108–125 (1965).
M. Green, Holomorphic maps into complex projective space omitting hyperplanes. Trans. Amer. Math. Soc. 169, 89–103 (1972).
M. Green, Holomorphic maps into complex tori. Amer. J. Math. 100, 615–620 (1978).
P. Griffiths, Complex differential and integral geometry and curvature integrals associated to singularities of complex analytic varieties. Duke Math. J. 45, 427–512 (1978).
P. Griffiths, Holomorphic mappings into canonical algebraic varieties. Ann. of Math. (2) 93, 439–458 (1971).
P. Griffiths and J. Harris, Local differential geometry and algebraic geometry. Ann. Ec. Norm sup. (Dec. 1979).
P. Griffiths and J. Harris, On the variety of special linear systems on a general algebraic curve. Duke Math. J. to appear.
P. Griffiths and J. Harris, Principles of Algebraic Geometry. Wiley, New York, 1978.
S. Iitaka, On D-dimensions of algebraic varieties. J. Math. Soc. Japan 23, 356–373 (1971).
S. Kleiman, Rigorous foundations of Schubert’s enumerative calculus, in Mathematical developments arising from Hilbert’s problems. In Proc. of Symposia, AMS, Vol. 27.
S. Kobayashi, Intrinsic distances, measures and geometric function theory. Bull. Amer. Math. Soc. 82, 357–416 (1976).
S. Kobayashi and T. Ochiai, Mappings into compact complex manifolds with negative first Chem class. J. Math. Soc. Japan 23, 137–148 (1971).
A. Mayer, Families of K-3 surfaces.
S. Mori, Projective manifolds with ample tangent bundles. To appear.
J. Noguchi, Meromorphic mappings into a compact complex space. Hiroshima Math. J. 7 (2), 411–425 (1977).
T. Ochiai, On holomorphic curves in algebraic varieties with ample irregularity. Invent. Math. 43, S3–96 (1977).
E. Picard, Sur une propriété des fonctions uniformes, liées par une relation algébrique. Compt. Rend. 91, 724–726 (1880).
B. Saint-Donat, Projective models of K-3 surfaces.
F. Sakai, Symmetry powers of the cotangent bundle and classification of algebraic varieties. In Proc. Copenhagen Summer Meeting in Algebraic Geometry, 1978.
H. Wu, A remark on holomorphic sectional curvature. Indiana Math. J. 22, 1103–1108 (1972/73).
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Green, M., Griffiths, P. (1980). Two Applications of Algebraic Geometry to Entire Holomorphic Mappings. In: Hsiang, WY., Kobayashi, S., Singer, I.M., Wolf, J., Wu, HH., Weinstein, A. (eds) The Chern Symposium 1979. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8109-9_4
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DOI: https://doi.org/10.1007/978-1-4613-8109-9_4
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