Sur une conjecture de Mukai

Commentarii Mathematici Helvetici

Volumn 78, Issue 3, 2003, Pages 601-626

  Bonavero, Laurent ^a   Casagrande, Cinzia ^b   Debarre, Olivier ^c   Druel, Stéphane ^a  

^a INSTITUT FOURIER   (France)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c UNIVERSITÉ LOUIS PASTEUR   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041382944     PISSN: 00102571     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00014-003-0765-x     Document Type: Article

References (27)

1. [An85] T. Ando, On extremal rays of the higher dimensional varieties, Invent. Math. 81 (1985), 347-357.
2. [ABW92] M. Andreatta, E. Ballico and J. A. Wiśniewski, Vector bundles and adjunction, Internat. J. Math. 3 (1992), 331-340.
3. [AW98] M. Andreatta and J. A. Wiśniewski, Contractions of smooth varieties. II. Computations and applications, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 1 (1998), 343-360.
4. [Ba91] V. V. Batyrev, On the classification of smooth projective toric varieties, Tohoku Mathematical Journal 43 (1991), 569-585.
5. [Ba99] V. V. Batyrev, On the classification of toric Fano 4-folds, Journal of Mathematical Sciences (New York) 94 (1999), 1021-1050.
6. [BCW01] L. Bonavero, F. Campana and J. A. Wiśniewski, Variétés projectives complexes dont l'Éclatée en un point est de Fano, C.R. Acad. Sci. Paris, Ser. I 334 (2002), 463-468.
7. [Bri02] M. Brion, The cone of effective one-cycles of certain G-varieties, Prépublication math.AG/0211027 (2002).
8. [Ca03] C. Casagrande, Contractible classes in toric varieties, Math. Zeitschrift 243 (2003), 99-126.
9. [CMS00] K. Cho, Y. Miyaoka and N. Shepherd-Barron, Characterizations of projective space and applications to complex symplectic manifolds, Higher dimensional birational geometry (Kyoto, 1997), 1-88, Adv. Stud. Pure Math. 35, Math. Soc. Japan, Tokyo, 2002.
10. [Fu93] W. Fulton. Introduction to toric varieties, Annals of mathematics studies 131, Princeton University Press, 1993.
11. [GHS03] T. Graber, J. Harris and J. Starr, Families of rationally connected varieties, J. Amer. Math. Soc. 16 (2003), 57-67.
12. [Gr68] A. Grothendieck, Le groupe de Brauer. I. Algèbres d'Azumaya et interprétations diverses, Dix exposés sur la cohomologie des schémas, 46-66, North-Holland, Amsterdam; Masson, Paris, 1968.
13. [IP99] V. A. Iskovskikh and Yu. G. Prokhorov, Fano varieties, Algebraic geometry V, Encyclopaedia Math. Sci. 47, Springer-Verlag, Berlin, 1999.
14. [Ka89] Y. Kawamata, Small contractions of four dimensional algebraic manifolds, Math. Ann. 284 (1989), 595-600.
15. [Ke01] S. Kebekus, Characterizing the projective space after Cho, Miyaoka and Shepherd-Barron, Festschrift in honor of Hans Grauert. 147-155, Complex geometry (Göttingen, 2000), Springer, Berlin, 2002.
16. [Kl88] P. Kleinschmidt, A classification of toric varieties with few generators, Aequationes Math. 35 (1988), 254-266.
17. [Ko96] J. Kollár, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihre Grenzgebiete, 3. Folge, 032, Springer-Verlag, 1996.
18. [KMM92] J. Kollár, Y. Miyaoka and S. Mori, Rational Connectedness and Boundedness of Fano Manifolds. J. Diff. Geom. 36 (1992), 765-769.
19. [La83] R. Lazarsfeld, Some applications of the theory of positive vector bundles, Complete intersections (Acireale, 1983), 29-61, Lecture Notes in Math. 1092, Springer-Verlag, Berlin, 1984.
20. [MMS71] P. McMullen and G. C. Shephard, Convex Polytopes and the Upper Bound Conjecture, London Mathematical Society Lecture Note Series 3, Cambridge University Press, 1971.
21. [Mo79] S. Mori, Projective manifolds with ample tangent bundles, Ann. of Math. 110 (1979), 593-606.
22. [Mo82] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982), 133-176.
23. 2 ≥ 2, Manuscripta Math. 36 (1981), 147-162.
24. [Mu88] S. Mukai, Problems on characterization of the complex projective space, Birational geometry of algebraic varieties. Open problems, The 23rd Intern. Sympos. Division of Math., The Taniguchi Foundation. Kataka, 1988.
25. [Od88] T. Oda, Convex bodies and algebraic geometry, an introduction to the theory of toric varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, 015, Springer-Verlag, 1988.
26. [Wi90] J. A. Wiśniewski, On a conjecture of Mukai, Manuscripta Math. 68 (1990), 135-141.
27. [Wi91] J. A. Wiśniewski, On contractions of extremal rays of Fano manifolds, J. reine angew. Math. 417 (1991), 141-157.