zbMATH — the first resource for mathematics

A finiteness property of varieties of general type. (English) Zbl 0438.14011

14E05 Rational and birational maps
14C15 (Equivariant) Chow groups and rings; motives
14C20 Divisors, linear systems, invertible sheaves
14E30 Minimal model program (Mori theory, extremal rays)
14J10 Families, moduli, classification: algebraic theory
PDF BibTeX Cite
Full Text: DOI EuDML
[1] Bombieri, E.: Canonical models of surfaces of general type. Publ. Math.42, 171-220 (1972) · Zbl 0259.14005
[2] Deschamps, M.M., Menegaud, R.L.: Applications rationelles separables dominantes sur une variete du type general. Bull. Soc. Math. France106, 279-287 (1978)
[3] Deschamps, M.M., Menegaud, R.L.: Surfaces de type general dominees par une variete fixe. C.R. Acad. Sci. Paris Ser. A765, 288 (1979)
[4] Deschamps, M.M., Menegaud, R.L.: Surfaces de type general dominees par une variete fixe. II. C.R. Acad. Sci. Ser. A342, 7 (1980)
[5] Fujita, T.: On Kähler fibre spaces over curves. J. Math. Soc. Japan30, 779-794 (1978) · Zbl 0393.14006
[6] Fujita, T.: On semipositive line bundles (to appear) · Zbl 0477.14010
[7] Grauert, H., Riemenschneider, O.: Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen. Invent. Math.11, 263-292 (1970) · Zbl 0202.07602
[8] Griffiths, P.: The extension problem in complex analysis. II. Embeddings with positive normal bundle. Am. J. Math.88, 366-446 (1966) · Zbl 0147.07502
[9] Griffiths, P.: Periods of integrals on algebraic manifolds. III. Publ. Math. I.H.E.S.38, 125-180 (1970) · Zbl 0212.53503
[10] Grothendieck, A.: Technique de construction et theoremes d’existence en geometrie algebrique. IV. Fondement de la geometrie algebrique. Collected Bourbaki talks, Extraits du Seminaire Bourbaki, 1957-1962 mimeo. notes, Secr. Math., Paris (1962)
[11] Grothendieck, A., Dieudonné, J.: Elements de geometrie algebrique. I?IV. Publ. Math. I.H.E.S.4,8, 11, 20, 21, 28, 32 (1960-1969)
[12] Hartshorne, R.: Algebraic geometry. In: Graduate Tests in Mathematics, Vol. 52. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0367.14001
[13] Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero. I. Ann. Math.79, 109-326 (1964) · Zbl 0122.38603
[14] Iitaka, S.: OnD-dimensions of algebraic varieties. J. Math. Soc. Japan23, 356-373 (1971) · Zbl 0212.53802
[15] Iitaka, S.: Algebraic geometry?an introduction to birational geometry of algebraic varieties. In: Graduate Texts in Mathematics, Vol. 76. Berlin, Heidelberg, New York: Springer 1981 · Zbl 0491.14005
[16] Jussila, O.: Formalisme des intersections sur les schemas algebraiques propres. Fx. X, SGA 6. In: Lecture Notes in Mathematics, Vol. 225. Berlin, Heidelberg, New York: Springer 1971
[17] Kawamata, Y.: Characterization of abelian varieties. Compositio Math.43, 253-276 (1981) · Zbl 0471.14022
[18] Kawamata, Y.: Kodaira dimension of algebraic fibre spaces over curves. Invent. Math.66, 57-71 (1982) · Zbl 0477.14011
[19] Kawamata, Y.: A generalization of Kodaira-Ramanujam’s vanishing theorem · Zbl 0476.14007
[20] Kleiman, S.: Les theoremes de finitude pour le foncteur de Picard. Fx. X, SGA 6. In: Lecture Notes in Mathematics. Berlin, Heidelberg, New York: Springer 1971
[21] Kodaira, K.: Pluricanonical systems on algebraic surfaces of general type. J. Math. Soc. Japan20 (1968) · Zbl 0157.27704
[22] Kodaira, K.: Holomorphic mappings of polydiscs into compact complex manifolds. J. Differential Geometry6, 33-46 (1971) · Zbl 0227.32008
[23] Kobayashi, S., Ochiai, T.: Meromorphic mappings into complex spaces of general type. Invent. Math.31, 7-16 (1975) · Zbl 0331.32020
[24] Kurke, H.: An algebraic proof of a theorem of S. Kobayashi and T. Ochiai, Forschungsinstitut für Mathematik ETH, Zürich (1978)
[25] Lieberman, D., Mumford, D.: Matsusaka’s big theorem in algebraic geometry (Arcata, 1974). Proc. Symp. Pure Math.29, 513 (1975)
[26] Mabuchi, T.: Invariant ? and uniruled threefold (to appear) · Zbl 0511.32016
[27] Maehara, K.: Family of varieties dominated by a variety. Proc. J. Acad.55 (A), 146-151 (1979) · Zbl 0432.14003
[28] Matsusaka, T., Mumford, D.: Two fundamental theorems on deformations of polarized varieties. Am. J. Math.89, 94-104 (1967) · Zbl 0146.42403
[29] Matsusaka, T.: Polarized varieties with a given Hilbert polynomial. Am. J. Math.94, 1027 (1972) · Zbl 0256.14004
[30] Mumford, D., Kempf, G., Knudsen, F., Sain-Donat, B.: Toroidal embeddings. I. In: Lecture Notes in Mathematics, Vol. 339. Berlin, Heidelberg, New York: Springer 1973 · Zbl 0271.14017
[31] Ramanujam, C.P.: Remarks on Kodaira vanishing theorem. J. Ind. Math. Soc.36, 41-51 (1972) · Zbl 0276.32018
[32] Samuel, P.: Complements a un article de Hans Grauert sur la conjecturé de Mordell. Publ. Math. I.H.E.S.29 (1966) · Zbl 0144.20102
[33] Schmid, W.: Variation of Hodge structure (the singularities of the period mapping). Invent. Math.22, 211-319 (1973) · Zbl 0278.14003
[34] Shioda, T.: Some results on unirationality of algebraic surfaces. Math. Ann.230, 153-168 (1977) · Zbl 0353.14021
[35] Szpiro: Sur le theoreme de rigidite d’Arakelov et Parsin. Journées de geometrie algebraique de Rennes. Astérisque64, 169 (1979)
[36] Ueno, K.: Classification theory of algebraic varieties and compact complex spaces. In: Lecture Notes in Mathematics, Vol. 439. Berlin Heidelberg, New York: Springer 1975 · Zbl 0299.14007
[37] Vieweg, E.: Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces (to appear)
[38] Weil, A.: Foundation of algebraic geometry. Am. Math. Soc.29 · Zbl 0168.18701
[39] Wilson, P.: The pluri-canonical maps on varieties of general type. Bull. Lond. Math. Soc.12, 103-107 (1980) · Zbl 0422.14005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.