Journal of Differential Geometry

Projectivity of complete moduli

János Kollár

Full-text: Open access

Article information

Source
J. Differential Geom. Volume 32, Number 1 (1990), 235-268.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214445046

Digital Object Identifier
doi:10.4310/jdg/1214445046

Mathematical Reviews number (MathSciNet)
MR1064874

Zentralblatt MATH identifier
0684.14002

Subjects
Primary: 14D22: Fine and coarse moduli spaces
Secondary: 14H10: Families, moduli (algebraic) 14J10: Families, moduli, classification: algebraic theory

Citation

Kollár, János. Projectivity of complete moduli. J. Differential Geom. 32 (1990), no. 1, 235--268. doi:10.4310/jdg/1214445046. https://projecteuclid.org/euclid.jdg/1214445046


Export citation

References

  • [1] A. Altman and S. Kleiman, Compactifying the Picard scheme. I, Advances in Math. 35 (1980) 50-112; II, Amer. J. Math. 101 (1979) 10-41.
  • [2] S. Arakelov, Families of algebraic curves with fixed degeneracies, Izv. Akad. Nauk SSSR 35 (1971) 1269-1293.
  • [3] M. Artin, Versaldeformations and algebraic stacks, Invent. Math. 27 (1974) 165-189.
  • [4] M. Artin, Algebraisation of formal moduli. II, Ann. of Math. (2) 91 (1970) 88-135.
  • [5] M. Artin and G. Winters, Degenerate fibers and stable reduction of curves, Topology 10 (1971) 373-384.
  • [6] C. Barton, Tensor products of ample vector bundles in characteristic p, Amer. J. Math. 93 (1971) 429-438.
  • [7] E. Bombieri and D. Mumford, Enriques' classification of surfaces in characteristic p. II, Complex Analysis and Algebraic Geometry, Cambridge Univ. Press, 1977, 23-42.
  • [8] P. Deligne and D. Mumford, The irreducibility of space of curves of given genus, Inst. Hautes Etudes Sci. Publ. Math. 36 (1969) 75-110.
  • [9] T. Ekedahl, Canonical models of surfaces of general type in positive characteristic, Inst. Hautes Etudes Sci. Publ. Math. 67 (1989) 97-144.
  • [10] T. Fujita, Kaehler fiber spaces over curves, J. Math. Soc. Japan 30 (1978) 779-794.
  • [11] R. Hartshorne, Ample vector bundles, Inst. Hautes Etudes Sci. Publ. Math. 29 (1966) 63-94.
  • [12] H. Hironaka, Resolution of singularities of an algebraicvarietyoverafield ofcharacteristic zero, Ann. of Math. (2) 79 (1964) 109-326.
  • [13] J. Igusa, Betti and Picard numbers of abstract algebraic surfaces, Prac. Nat. Acad. Sci. U.S.A. 46 (1960) 724-726.
  • [14] Y. Kawamata, Kodaira dimension of algebraic fiber spaces over curves, Invent. Math. 66 (1982) 57-71.
  • [15] Y. Kawamata, Thecrepant blowing-up of 3-dimensional canonical singularities and its application to the degeneration of surfaces, Ann. of Math. (2) 127 (1988) 93-163.
  • [16] S. Kleiman, Towarda numerical theory of ampleness, Ann. of Math. (2) 84 (1966) 293-344.
  • [17] F. Knudsen and D. Mumford, The projectivity of the moduli space of stable curves. I, Math. Scand. 39 (1976) 19-55.
  • [18] F. Knudsen, The projectivity of the moduli space of stable curves, II--III, Math. Scand. 52 (1983) 161-212.
  • [19] D. Knutson, Algebraic spaces, Lecture Notes in Math., Vol. 203. Springer, Berlin, 1971.
  • [20] J. Kollar, Toward moduli of singular varieties, Compositio Math. 56 (1985) 369-398.
  • [21] J. Kollar, Higher direct images of dualizing sheaves. II, Ann. of Math. (2) 124 (1986) 171--202.
  • [22] J. Kollar, Subadditivity of the Kodaira dimension: Fibers of general type, Algebraic Geometry, Sendai 1985, Advanced Studies in Pure Math., Vol. 10, Kinokuniya-North Holland, 1987, 361-398.
  • [23] J. Kollar and N. I. Shepherd-Barron, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988) 299-338.
  • [24] B. Moishezon, A criterion for projectivity of complete abstract algebraic varieties, Amer. Math. Soc. Transl. 63 (1967) 1-50.
  • [25] L. Moret-Bailly, Families de Courbes et de Varietes Abeliennes, Asterisque 86 (1981) 125-140.
  • [26] D. Mumford, Stability of projective varieties, Enseignement Math. 23 (1977) 39-110.
  • [27] D. Mumford and J. Fogarthy, Geometric invariant theory, 2nd edition, Springer, Berlin, 1982.
  • [28] Y. Nakai, A criterion of ample sheaf on a projective scheme, Amer. J. Math. 85 (1963) 14-26.
  • [29] M. Reid, Canonical threefolds, in Geometrie Algebrique Angers (A. Beauville, ed.), Sijthoff and Noordhoff, Alphen aan den Rijn, 1980, 273-310.
  • [30] N. I. Shepherd-Barron, Degenerations with numerically effective canonical divisor, The Birational Theory of Degenerations, Birkhauser, Boston, 1983, 33-84.
  • [31] D. van Straten, Weakly normal surface singularities and their improvements, Thesis, Leiden, 1987 (to appear).
  • [32] L. Szpiro, Proprietes numerique dufaisceau dualisant relatif, Asterisque 86 (1981) 44-78.
  • [33] E. Viehweg, Weakpositivity and the additivity of the Kodaira dimension. I, Algebraic Varieties and Analytic Varieties, Advanced Studies in Pure Math., Vol. 1, Kinokuniya- North Holland, 1983, 329-353; II, Classification of Algebraic and Analytic Manifolds, Birkhauser, Boston, 1983, 567-590.
  • [34] E. Viehweg, Weak positivity and the stability of certain Hilbert points, Invent. Math. 96 (1989), 639-667.