Abstract.
We rule out a doubtful case in the classification of Fano manifolds of middle index
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Andreatta, M., Chierici, E., Occhetta, G.: Generalized Mukai conjecture for special Fano varieties. CEJM 2 (2), 272–293 (2004)
Andreatta, M., Wiśniewski, J.A.: On manifolds whose tangent bundle contains an ample subbundle. Invent. Math. 146 (1), 209–217 (2001)
Ballico, E., Wiśniewski, J.A.: On Banica sheaves and Fano manifolds. Compositio Math. 102 (3), 313–335 (1996)
Campana, F.: Connexité rationnelle des variétés de Fano. Ann. Sci. École Norm. Sup. 25, 539–545 (1992)
Chierici, E., Occhetta, G.: The cone of curves of Fano varieties of coindex four. Preprint math.AG/0401429
Cho, K., Miyaoka, Y., Shepherd-Barron, N.: Characterizations of projective space and applications to complex symplectic manifolds. Higher dimensional birational geometry (Kyoto, 1997), Adv. Studies in Pure Math. Vol. 35, Math. Soc. Japan, Tokyo, 2002, pp. 1–88
Kebekus, S.: Characterizing the projective space after Cho, Miyaoka and Sheperd-Barron. Complex Geometry, Göttingen 2000, Springer Berlin, 2002, pp. 147–155
Kollár, J.: Rational curves on algebraic varieties. Ergebnisse der Math. Vol. 32, Springer Verlag, Berlin, Heidelberg, New York, Tokio, 1996
Miyaoka, Y.: Numerical characterisations of hyperquadrics. Complex analysis in several variables–-Memorial Conference of Kiyoshi Oka’s Centennial Birthday, Adv. Stud. Pure Math. 42, Math. Soc. Japan, Tokyo, 2004, pp. 209–235
Miyaoka, Y.: Numerical characterisations of hyperquadrics. Proceedings of The Fano Conference, on 50th anniversary of death of Gino Fano, (ed.), Collino, Conte, Marchisio, Univ. Torino 2004, pp. 559–561
Mori, S.: Projective manifolds with ample tangent bundle. Ann. Math. 110, 595–606 (1979)
Peternell, T., Szurek, M., Wiśniewski, J.A.: Fano manifolds and vector bundles. Math. Ann. 294, 151–165 (1992)
Sato, E.: Varieties which have two projective space bundle structures. J. Math. Kyoto Univ. 25 (3), 445–457 (1985)
Wiśniewski, J.A.: On a conjecture of Mukai. Manuscripta Math. 68, 135–141 (1990)
Wiśniewski, J.A.: On Fano manifolds of large index. Manuscripta Math. 70, 145–152 (1991)
Wiśniewski, J.A.: Fano manifolds and quadric bundles. Math. Z. 214, 261–271 (1993)
Wiśniewski, J.A.: A report on Fano manifolds of middle index and b2≥ 2. Projective geometry with applications (Dekker, New York), Lecture Notes in Pure and Appl. Math. Vol. 166, 1994, pp. 19–26
Author information
Authors and Affiliations
Corresponding author
Additional information
Mathematics Subject Classification (2000): 14J40, 14J45
Rights and permissions
About this article
Cite this article
Occhetta, G. A note on the classification of Fano manifolds of middle index. manuscripta math. 117, 43–49 (2005). https://doi.org/10.1007/s00229-005-0540-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-005-0540-y