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

Colloquium Mathematicae (1993)

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

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topDobrowolska, 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

top- [1] G. Elencwajg and O. Forster, Bounding cohomology groups of vector bundles on ${\mathbb{P}}_{n}$, Math. Ann. 246 (1980), 251-270. Zbl0432.14011
- [2] H. J. Hoppe, Generischer Spaltungstyp und zweite Chernklasse stabiler Vektorraumbündel vom Rang 4 auf ${\mathbb{P}}_{4}$, Math. Z. 187 (1984), 345-360. Zbl0567.14011
- [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] M. Maruyama, The theorem of Grauert-Mülich-Spindler, Math. Ann. 255 (1981), 317-333. Zbl0438.14015
- [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. Zbl0432.14012

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