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2004 | 2 | 2 | 272-293
Tytuł artykułu

Generalized Mukai conjecture for special Fano varieties

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let X be a Fano variety of dimension n, pseudoindex i X and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(i X−1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i X≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
2
Strony
272-293
Opis fizyczny
Daty
wydano
2004-04-01
online
2004-04-01
Twórcy
Bibliografia
  • [1] M. Andreatta and J.A. Wiśniewski: “On manifolds whose tangent bundle contains an ample subbundle”, Invent. Math., Vol. 146, (2001), pp. 209–217. http://dx.doi.org/10.1007/PL00005808
  • [2] L. Bonavero, C. Casagrande, O. Debarre and S. Druel: “Sur une conjecture de Mukai”, Comment. Math. Helv., Vol. 78, (2003), pp. 601–626. http://dx.doi.org/10.1007/s00014-003-0765-x
  • [3] L. Bonavero, F. Campana and J.A. Wiśniewski: “Variétés complexes dont l'éclat'ee en un point est de Fano”, C.R. Math. Acad. Sci. Paris, Vol. 334, (2002), pp. 463–468.
  • [4] F. Campana: “Connexité rationnelle des variétés de Fano”, Ann. Sci. École Norm. Sup., Vol. 25, (1992), pp. 539–545.
  • [5] K. Cho, Y. Miyaoka and N.I. Shepherd-Barron: “Characterizations of projective space and applications to complex symplectic manifolds”, in: Higher dimensional birational geometry (Kyoto, 1997) Adv. Stud. Pure Math., Vol. 35, Math. Soc. Japan, Tokyo, 2002, pp. 1–88.
  • [6] O. Debarre: Higher-Dimensional Algebraic Geometry, Universitext Springer-Verlag, New York, 2001.
  • [7] S. Kebekus: “Characterizing the projective space after Cho, Miyaoka and Shepherd-Barron”, In: Complex geometry (Göttingen, 2000), Springer, Berlin, 2002, pp. 147–155.
  • [8] J. Kollár: Rational Curves on Algebraic Varieties, Ergebnisse der Math. Vol. 32, Springer-Verlag, 1996.
  • [9] J. Kollár, Y. Miyaoka and S. Mori: “Rational connectedness and boundedness of Fano manifolds”, J. Diff. Geom. Vol. 36, (1992), pp. 765–779.
  • [10] S. Mori: “Projective manifolds with ample tangent bundle”, Ann. Math., Vol. 110, (1979), pp. 595–606. http://dx.doi.org/10.2307/1971241
  • [11] S. Mukai: “Open problems”, In: Birational geometry of algebraic varieties, Taniguchi Foundation, Katata, 1988.
  • [12] G. Occhetta: A characterization of products of projective spaces, preprint, February 2003, http://www.science.unitn.it/∼occhetta.
  • [13] J.A. Wiśniewski: “On a conjecture of Mukai”, Manuscripta Math., Vol. 68, (1990), pp. 135–141.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02476544
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