Geodesic
A Characterization of Products of Projective Spaces
Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 270-280

Voir la notice de l'article provenant de la source Cambridge University Press

We give a characterization of products of projective spaces using unsplit covering families of rational curves.
DOI : 10.4153/CMB-2006-028-3
Mots-clés : 14J40, 14J45, Rational curves, Fano varieties 
Occhetta, Gianluca. A Characterization of Products of Projective Spaces. Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 270-280. doi: 10.4153/CMB-2006-028-3
@article{10_4153_CMB_2006_028_3,
     author = {Occhetta, Gianluca},
     title = {A {Characterization} of {Products} of {Projective} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {270--280},
     year = {2006},
     volume = {49},
     number = {2},
     doi = {10.4153/CMB-2006-028-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-028-3/}
}
TY  - JOUR
AU  - Occhetta, Gianluca
TI  - A Characterization of Products of Projective Spaces
JO  - Canadian mathematical bulletin
PY  - 2006
SP  - 270
EP  - 280
VL  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-028-3/
DO  - 10.4153/CMB-2006-028-3
ID  - 10_4153_CMB_2006_028_3
ER  - 
%0 Journal Article
%A Occhetta, Gianluca
%T A Characterization of Products of Projective Spaces
%J Canadian mathematical bulletin
%D 2006
%P 270-280
%V 49
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-028-3/
%R 10.4153/CMB-2006-028-3
%F 10_4153_CMB_2006_028_3

[1] [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] [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] [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] [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] [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] [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] [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] [8] Kollár, J., Rational Curves on Algebraic Varieties, Ergebnisse derMathematik und ihrer Grenzgebiete 32, Springer-Verlag, Berlin, 1996. Google Scholar

[9] [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] [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] [11] Wiśniewski, J. A., On a conjecture of Mukai. Manuscripta Math. 68(1990), no. 2, 135–141. Google Scholar

Cité par Sources :