This work concerns bounds for Chern classes of holomorphic semistable and stable vector bundles on . Non-negative polynomials in Chern classes are constructed for 4-vector bundles on and a generalization of the presented method to r-bundles on is given. At the end of this paper the construction of bundles from complete intersection is introduced to see how rough the estimates we obtain are.
@article{bwmeta1.element.bwnjournal-article-cmv65i2p277bwm,
author = {Wiera Dobrowolska},
title = {Bounds for Chern classes of semistable vector bundles on complex projective spaces},
journal = {Colloquium Mathematicae},
volume = {66},
year = {1993},
pages = {277-290},
zbl = {0832.14006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv65i2p277bwm}
}
Dobrowolska, Wiera. Bounds for Chern classes of semistable vector bundles on complex projective spaces. Colloquium Mathematicae, Tome 66 (1993) pp. 277-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv65i2p277bwm/
[000] [1] G. Elencwajg and O. Forster, Bounding cohomology groups of vector bundles on , Math. Ann. 246 (1980), 251-270. | Zbl 0432.14011
[001] [2] H. J. Hoppe, Generischer Spaltungstyp und zweite Chernklasse stabiler Vektorraumbündel vom Rang 4 auf , Math. Z. 187 (1984), 345-360. | Zbl 0567.14011
[002] [3] K. Jaczewski, M. Szurek and J. Wiśniewski, Geometry of the Tango bundle, in: Proc. Conf. Algebraic Geometry, Berlin 1985, Teubner-Texte Math. 92, Teubner, 1986, 177-185. | Zbl 0628.14015
[003] [4] M. Maruyama, The theorem of Grauert-Mülich-Spindler, Math. Ann. 255 (1981), 317-333. | Zbl 0438.14015
[004] [5] C. Okonek, M. Schneider and H. Spindler, Vector Bundles on Complex Projective Spaces, Progr. Math. 3, Birkhäuser, 1980.
[005] [6] M. Schneider, Chernklassen semi-stabiler Vektorraumbündel vom Rang 3 auf dem komplex-projektiven Raum, J. Reine Angew. Math. 315 (1980), 211-220. | Zbl 0432.14012