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

Wiera Dobrowolska

Colloquium Mathematicae (1993)

  • Volume: 65, Issue: 2, page 277-290
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Dobrowolska, Wiera. "Bounds for Chern classes of semistable vector bundles on complex projective spaces." Colloquium Mathematicae 65.2 (1993): 277-290. <http://eudml.org/doc/210221>.

@article{Dobrowolska1993,
abstract = {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.},
author = {Dobrowolska, Wiera},
journal = {Colloquium Mathematicae},
keywords = {Chern classes; rank 4 vector bundle},
language = {eng},
number = {2},
pages = {277-290},
title = {Bounds for Chern classes of semistable vector bundles on complex projective spaces},
url = {http://eudml.org/doc/210221},
volume = {65},
year = {1993},
}

TY - JOUR
AU - Dobrowolska, Wiera
TI - Bounds for Chern classes of semistable vector bundles on complex projective spaces
JO - Colloquium Mathematicae
PY - 1993
VL - 65
IS - 2
SP - 277
EP - 290
AB - 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.
LA - eng
KW - Chern classes; rank 4 vector bundle
UR - http://eudml.org/doc/210221
ER -

References

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  1. [1] G. Elencwajg and O. Forster, Bounding cohomology groups of vector bundles on ℙ n , Math. Ann. 246 (1980), 251-270. Zbl0432.14011
  2. [2] H. J. Hoppe, Generischer Spaltungstyp und zweite Chernklasse stabiler Vektorraumbündel vom Rang 4 auf ℙ 4 , Math. Z. 187 (1984), 345-360. Zbl0567.14011
  3. [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. Zbl0628.14015
  4. [4] M. Maruyama, The theorem of Grauert-Mülich-Spindler, Math. Ann. 255 (1981), 317-333. Zbl0438.14015
  5. [5] C. Okonek, M. Schneider and H. Spindler, Vector Bundles on Complex Projective Spaces, Progr. Math. 3, Birkhäuser, 1980. 
  6. [6] M. Schneider, Chernklassen semi-stabiler Vektorraumbündel vom Rang 3 auf dem komplex-projektiven Raum, J. Reine Angew. Math. 315 (1980), 211-220. Zbl0432.14012

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