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2006 | 4 | 2 | 209-224
Tytuł artykułu

Subsheaves of the cotangent bundle

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For any smooth projective variety, we study a birational invariant, defined by Campana which depends on the Kodaira dimension of the subsheaves of the cotangent bundle of the variety and its exterior powers. We provide new bounds for a related invariant in any dimension and in particular we show that it is equal to the Kodaira dimension of the variety, in dimension up to 4, if this is not negative.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
2
Strony
209-224
Opis fizyczny
Daty
wydano
2006-06-01
online
2006-06-01
Twórcy
Bibliografia
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  • [2] S. Boucksom, J.P. Demailly, M. Paun and T. Peternell: “The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension”, math.AG/0405285.
  • [3] F. Campana: “Réducation d’Albanèse d’un morphisme propre et faiblement kählérien. II. Groupes d’automorphismes relatifs”, Compositio Math., Vol. 54(3), (1985), pp. 399–416.
  • [4] F. Campana: “Connexité rationelle des variétés de Fano”, Ann. Sci. E.N.S., Vol. 25, (1992), pp. 539–545.
  • [5] F. Campana: “Fundamental Group and Positivity of Cotangent Bundles of Compact Kähler Manifolds”, J. Algebraic Geom., Vol. 4, (1995), pp. 487–502.
  • [6] F. Campana: “Orbifolds, Special Varieties and Classification Theory”, Ann. Inst. Fourier, Grenoble, Vol. 54(3), (2004), pp. 499–630.
  • [7] F. Campana and T. Peternell: “Geometric Stability of the Cotangent Bundle and the Universal Cover of a Projective Manifold”, math.AG/0405093.
  • [8] J.P. Demailly, T. Peternell and M. Schneider: “Pseudo-effective Line Bundles on compact Kähler Manifolds”, Intern. J. Math., Vol. 12(6), (2001), pp. 689–741.
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  • [17] J. Kollár: Shafarevich maps and automorphic forms, Princeton University Press, 1995.
  • [18] K. Matsuki, Introduction to the Mori program, Springer-Verlag, New York, 2002.
  • [19] Y. Miyaoka: “The Chern classes and Kodaira dimension of a minimal variety”, In: Proc. Sympos. Alg. Geom., Sendai 1985, Adv. Stud. Pure Math, Vol. 10, Kynokuniya, Tokyo, 1985, pp. 449–476.
  • [20] S. Mori: “Classification of higher-dimensional varieties”, In: Algebraic geometry, Bowdoin 1985 (Brunswick/Maine 1985), Proc. Symp. Pure Math., Vol. 46(1), Amer. Math. Soc., Providence, RI, 1987, pp. 269–331.
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  • [24] E. Viehweg: “Die Additivität der Kodaira Dimension für projektive Faserräume über Varietäten des allgemeinen Typs”, J. Reine Angew. Math., Vol. 330, (1982), pp. 132–142.
  • [25] E. Viehweg and K. Zuo: “On the isotriviality of families of projective manifolds over curves Complex Spaces”, J. Alg. Geom., Vol. 10, (2001), pp. 781–799.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-006-0003-z
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