Article PDF
Avoid common mistakes on your manuscript.
References
Boucksom S., Demailly J.-P., Păun M., Peternell T.: The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension. arXiv:arch-ive/0405285 (2004)
Boucksom S.: Cônes positifs des variétés complexes compactes, Thesis, Grenoble (2002)
Bruzzo U., Hernández Ruipérez D.: Semistability vs. nefness for (Higgs) vector bundles. Differ. Geom. Appl. 24(4), 403–416 (2006)
Campana F., Peternell T.: Algebraicity of the ample cone of projective varieties. J. Reine Angew. Math. 407, 160–166 (1990)
Chen H.: Computing volume function on projective bundle over a curve. http://hal.archives-ouvertes.fr/hal-00295905/en/ (2008)
Fulton W.: Intersection Theory, 2nd ed., Ergebnisse der Math. und ihrer Grenzgebiete (3), vol. 2. Springer, Berlin (1998)
Hartshorne R.: Algebraic Geometry, Graduate Texts in Math., vol. 52. Springer, New York (1977)
Hartshorne R.: Ample vector bundles on curves. Nagoya Math. J. 43, 73–89 (1971)
Kawamata Y.: The cone of curves of algebraic varieties. Ann. Math. (2) 119(3), 603–633 (1984)
Kleiman S.L.: Toward a numerical theory of ampleness. Ann. Math. (2) 84, 293–344 (1966)
Lazarsfeld, R.: Positivity in Algebraic Geometry I, Classical Setting: Line Bundles and Linear Series, Ergebnisse der Math. und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, 48. Springer, Berlin (2004)
Lazarsfeld, R.: Positivity in Algebraic Geometry II, Positivity for Vector Bundles, and Multiplier Ideals, Ergebnisse der Math. und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, 49. Springer, Berlin (2004)
Le Potier J.: Lectures on Vector Bundles. Cambridge University Press, Cambridge (1997)
Mehta V.B., Ramanathan A.: Semistable sheaves on projective varieties and their restriction to curves. Math. Ann. 258, 213–224 (1982)
Miyaoka Y.: The Chern classes and Kodaira dimension of a minimal variety, in: Algebraic Geometry, Sendai 1985. Adv. Stud. Pure Math. 10, 449–476 (1987)
Okonek, C., Schneider, M., Spindler, H.: Vector Bundles on Complex Projective Spaces, Progress in Mathematics, vol. 3, Birkhäuser Boston (1980)
Wolfe, A.: Asymptotic invariants of graded systems of ideals and linear systems on projective bundles, Ph.D. Thesis, University of Michigan (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fulger, M. The cones of effective cycles on projective bundles over curves. Math. Z. 269, 449–459 (2011). https://doi.org/10.1007/s00209-010-0744-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00209-010-0744-z