Bounds for Chern classes of semistable vector bundles on complex projective spaces

• Autorzy: Wiera Barbara Dobrowolska
• Języki publikacji: EN

Abstrakty

EN

This work concerns bounds for Chern classes of holomorphic semistable and stable vector bundles on $ℙ^n$. Non-negative polynomials in Chern classes are constructed for 4-vector bundles on $ℙ^4$ and a generalization of the presented method to r-bundles on $ℙ^n$ 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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 65
• Numer: 2
• Strony: 277-290

Daty

wydano

1993

otrzymano

1992-05-28

poprawiono

1993-02-16

Twórcy

autor

Wiera Barbara Dobrowolska

• Institute of Theoretical and Applied Computer Science, Polish Academy of Sciences, Bałtycka 5, 44-100 Gliwice, Poland

Bibliografia

• [1] G. Elencwajg and O. Forster, Bounding cohomology groups of vector bundles on $ℙ_n$, Math. Ann. 246 (1980), 251-270.
• [2] H. J. Hoppe, Generischer Spaltungstyp und zweite Chernklasse stabiler Vektorraumbündel vom Rang 4 auf $ℙ_4$, Math. Z. 187 (1984), 345-360.
• [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.
• [4] M. Maruyama, The theorem of Grauert-Mülich-Spindler, Math. Ann. 255 (1981), 317-333.
• [5] C. Okonek, M. Schneider and H. Spindler, Vector Bundles on Complex Projective Spaces, Progr. Math. 3, Birkhäuser, 1980.
• [6] M. Schneider, Chernklassen semi-stabiler Vektorraumbündel vom Rang 3 auf dem komplex-projektiven Raum, J. Reine Angew. Math. 315 (1980), 211-220.