# On simple and stable homogeneous bundles

Bollettino dell'Unione Matematica Italiana (2006)

- Volume: 9-B, Issue: 1, page 51-67
- ISSN: 0392-4033

## Access Full Article

top## Abstract

top## How to cite

topFaini, Simona. "On simple and stable homogeneous bundles." Bollettino dell'Unione Matematica Italiana 9-B.1 (2006): 51-67. <http://eudml.org/doc/289620>.

@article{Faini2006,

abstract = {In this work we will analyze the relation between the stability and the simplicity of a homogeneous vector bundle on a projective variety. Our main theorem shows that a homogeneous bundle is not destabilized by its homogeneous subbundles if and only if it is the tensor product of a stable homogeneous bundle and an irreducible representation. Then we give an example of a homogeneous bundle, which is simple, but not stable.},

author = {Faini, Simona},

journal = {Bollettino dell'Unione Matematica Italiana},

language = {eng},

month = {2},

number = {1},

pages = {51-67},

publisher = {Unione Matematica Italiana},

title = {On simple and stable homogeneous bundles},

url = {http://eudml.org/doc/289620},

volume = {9-B},

year = {2006},

}

TY - JOUR

AU - Faini, Simona

TI - On simple and stable homogeneous bundles

JO - Bollettino dell'Unione Matematica Italiana

DA - 2006/2//

PB - Unione Matematica Italiana

VL - 9-B

IS - 1

SP - 51

EP - 67

AB - In this work we will analyze the relation between the stability and the simplicity of a homogeneous vector bundle on a projective variety. Our main theorem shows that a homogeneous bundle is not destabilized by its homogeneous subbundles if and only if it is the tensor product of a stable homogeneous bundle and an irreducible representation. Then we give an example of a homogeneous bundle, which is simple, but not stable.

LA - eng

UR - http://eudml.org/doc/289620

ER -

## References

top- ANCONA, V., Fibrati vettoriali su varieta razionali omogenee, Boll. UMI, 7 (1988), 299-317.
- ATIYAH, M., On the Krull-Schmidt theorem with application to sheaves, Bull. Soc. Math. France, 84 (1956), 306-317. Zbl0072.18101MR86358
- FAINI, S., Stabilità e semplicità dei fibrati omogenei su $\u2102{\mathbb{P}}^{2}$, tesi di laurea, Firenze, 2002.
- MIGLIORINI, L., Stability of homogeneous vector bundles, Boll. UMI, Ser. VII, B 10, nr. 4 (1996), 963-990. Zbl0885.14024MR1430162
- OKONEK, C. - SCHNEIDER, M. - SPINDLER, H., Vector bundles on complex projective spaces, Birkhäuser, Boston, 1980. Zbl0438.32016MR561910
- OTTAVIANI, G., Rational homogeneous varieties, notes for the SMI-course in Cortona,1995 (available at http://www.math.unifi.it/~ottavian).
- PAOLETTI, R., Stability of a class of homogeneous vector bundles on $\u2102{\mathbb{P}}^{n}$, Boll. UMI,Ser. VII, A 9, nr. 2 (1995), 329-343. Zbl0888.14006MR1336240
- RAMANAN, S., Holomorphic vector bundles on homogeneous spaces, Topology, Vol. 5, pp. 159-177, Pergamon Press, 1966. Zbl0138.18602MR190947DOI10.1016/0040-9383(66)90017-6
- ROHMFELD, R., Stability of homogeneous vector bundles on $\u2102{\mathbb{P}}^{n}$, GeometriaeDedicata, 38 (1991), 159-166. Zbl0734.14004MR1104341DOI10.1007/BF00181215
- ROHMFELD, R., Stabile homogenen Vektorbündel über der komplexen projectiven Ebene, PHD-thesis, Erlangen, 1989.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.