Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T18:50:15.995Z Has data issue: false hasContentIssue false
  • English
  • Français

A Characterization of Products of Projective Spaces

Published online by Cambridge University Press:  20 November 2018

Gianluca Occhetta
Gianluca Occhetta*
Affiliation:
Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive, 14, I-38050 Povo (Trento), Italy e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a characterization of products of projective spaces using unsplit covering families of rational curves.

Keywords

14J4014J45Rational curvesFano varieties
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 2 , 01 June 2006 , pp. 270 - 280
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Andreatta, M., and Wiśniewski, J. A., A view on contractions of higher dimensional varieties. In: Algebraic Geometry, Proc. Sympos. Pure Math. 62, American Mathematical Society, Providence, RI, 1997, pp. 153–183.Google Scholar
[2] Andreatta, M., and Wiśniewski, J. A., On manifolds whose tangent bundle contains an ample subbundle. Invent. Math. 146(2001), no. 1, 209–217.Google Scholar
[3] Beltrametti, M. C., Sommese, A. J., and Wiśniewski, J. A., Results on varieties with many lines and their applications to adjunction theory. In: Complex Algebraic Varieties 1507, Lecture Notes in Math. 1507, Springer, Berlin, 1992, pp. 16–38.Google Scholar
[4] Bonavero, L., Casagrande, C., Debarre, O., and Druel, S., Sur une conjecture de Mukai. Comment. Math. Helv. 78(2003), no. 3, 601–626.Google Scholar
[5] Cho, K., Miyaoka, Y., and Shepherd-Barron, N., Characterizations of projective space and applications to complex symplectic manifolds. In: Higher Dimensional Birational Geometry, Adv. Stud. Pure Math. 35, Math. Soc. Japan, Tokyo, 2002, 1–88.Google Scholar
[6] Fujita, T., On polarized manifolds whose adjoint bundles are not semipositive. In: Algebraic Geometry, Adv. Stud. Pure Math. 10, North-Holland, Amsterdam, 1987, pp. 167–178.Google Scholar
[7] Kebekus, S., Characterizing the projective space after Cho, Miyaoka and Sheperd-Barron. In: Complex Geometry, Springer, Berlin, 2002, pp. 147–155.Google Scholar
[8] Kollár, J., Rational Curves on Algebraic Varieties, Ergebnisse derMathematik und ihrer Grenzgebiete 32, Springer-Verlag, Berlin, 1996.Google Scholar
[9] Lazarsfeld, R., Some applications of the theory of positive vector bundles. In: Complete Intersections, Lecture Notes in Math. 1092, Springer, Berlin, 1984, pp. 29–61.Google Scholar
[10] Mukai, S., Open problems. In: Birational Geometry of Algebraic Varieties, Cambridge Tracts in Mathematics 134, Cambridge University Press, Cambridge, 1988, pp. 67–60.Google Scholar
[11] Wiśniewski, J. A., On a conjecture of Mukai. Manuscripta Math. 68(1990), no. 2, 135–141.Google Scholar