Resolutions of homogeneous bundles on 2
[Résolutions des fibrés homogènes sur 2 .]
Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 973-1015.

Nous caractérisons les résolutions libres minimales des fibrés homogènes sur 2 et nous étudions la stabilité et la simplicité des fibrés homogènes sur 2 par leurs résolutions libres minimales. En particulier, nous établissons un critère de simplicité pour un fibré homogène dans le cas où le premier fibré de sa résolution minimale est irréductible.

We characterize minimal free resolutions of homogeneous bundles on 2 . Besides we study stability and simplicity of homogeneous bundles on 2 by means of their minimal free resolutions; in particular we give a criterion to see when a homogeneous bundle is simple by means of its minimal resolution in the case the first bundle of the resolution is irreducible.

DOI : 10.5802/aif.2119
Classification : 14M17, 14F05, 16G20
Keywords: homogeneous bundles, minimal resolutions, quivers
Mot clés : fibres homogènes, résolutions minimales, carquois
Ottaviani, Giorgio 1 ; Rubei, Elena 

1 Dipartimento di Matematica ``U.Dini'', Viale Morgagni 67/A, c.a.p., 50134 Firenze (Italy)
@article{AIF_2005__55_3_973_0,
     author = {Ottaviani, Giorgio and Rubei, Elena},
     title = {Resolutions of homogeneous bundles on ${\mathbb {P}}^2$},
     journal = {Annales de l'Institut Fourier},
     pages = {973--1015},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {55},
     number = {3},
     year = {2005},
     doi = {10.5802/aif.2119},
     mrnumber = {2149408},
     zbl = {1079.14051},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2119/}
}
TY  - JOUR
AU  - Ottaviani, Giorgio
AU  - Rubei, Elena
TI  - Resolutions of homogeneous bundles on ${\mathbb {P}}^2$
JO  - Annales de l'Institut Fourier
PY  - 2005
SP  - 973
EP  - 1015
VL  - 55
IS  - 3
PB  - Association des Annales de l’institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.2119/
DO  - 10.5802/aif.2119
LA  - en
ID  - AIF_2005__55_3_973_0
ER  - 
%0 Journal Article
%A Ottaviani, Giorgio
%A Rubei, Elena
%T Resolutions of homogeneous bundles on ${\mathbb {P}}^2$
%J Annales de l'Institut Fourier
%D 2005
%P 973-1015
%V 55
%N 3
%I Association des Annales de l’institut Fourier
%U http://archive.numdam.org/articles/10.5802/aif.2119/
%R 10.5802/aif.2119
%G en
%F AIF_2005__55_3_973_0
Ottaviani, Giorgio; Rubei, Elena. Resolutions of homogeneous bundles on ${\mathbb {P}}^2$. Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 973-1015. doi : 10.5802/aif.2119. http://archive.numdam.org/articles/10.5802/aif.2119/

[Ba] E. Ballico On the stability of certain higher rank bundles on n , Rend. Circ. Mat. Palermo, Volume 41 (1992) no. 2, pp. 309-314 | DOI | MR | Zbl

[BK] A.I. Bondal; M.M. Kapranov Homogeneous Bundles, Seminar Rudakov, Helices and Vector bundles (Lecture Notes Series of London Math. Soc.), Volume 148 (1990), pp. 45-55 | Zbl

[DL] J.-M. Drézet; J. Le Potier Fibrés stables et fibrés exeptionnels sur le plan projectif, Ann. Sci. École Norm. Sup., 4e série, Volume 18 (1985), pp. 193-244 | Numdam | MR | Zbl

[Fa] S. Faini On the stability and simplicity of homogeneous bundles (to appear in Boll. U.M.I.)

[FH] W. Fulton; J. Harris Representation Theory, A First Course,, Graduate Texts in Math., Springer Verlag, 1991 | MR | Zbl

[GR] P. Gabriel; A.V. Roiter Algebra VIII: Representations of finite dimensional algebras, Encyclopaedia of Mathematical Sciences, 73, Springer Verlag, 1992 | MR | Zbl

[Hi1] L. Hille Homogeneous vector bundles and Koszul algebras, Math. Nach., Volume 191 (1998), pp. 189-195 | DOI | MR | Zbl

[Hi2] L. Hille Small homogeneous vector bundles (1994) (Phd Thesis, Bielefeld) | Zbl

[Ho] G. Horrocks Vector bundles on the punctured spectrum of a local ring, Proc. London Math. Soc., Volume 14 (1964), pp. 689-713 | DOI | MR | Zbl

[Ka] M.M. Kapranov On the derived categories of coherent sheaves on some homogeneous spaces, Invent. Math., Volume 92 (1988), pp. 479-508 | DOI | MR | Zbl

[Ki] A. King Moduli of representations of finite-dimensional algebras, Quart. J. Math. Oxford Ser. (2), Volume 45 (1994) no. 180, pp. 515-530 | MR | Zbl

[Mi] L. Migliorini Stability of homogeneous bundles, Boll. Unione Mat. Ital. Sez. B, Volume 10 (1996), pp. 963-990 | MR | Zbl

[OR] G. Ottaviani; E. Rubei Quivers and the cohomology of homogeneous vector bundles (math.AG/0403307, http://arxiv.org/abs/math.AG/0403307)

[Ra] S. Ramanan Holomorphic vector bundles on homogeneous spaces, Topology, Volume 5 (1966), pp. 159-177 | DOI | MR | Zbl

[Ro] R. Rohmfeld Stability of homogeneous vector bundles on P n , Geom. Dedicata, Volume 38 (1991), pp. 159-166 | MR | Zbl

[Si] D. Simpson Linear representation of quivers (Lectures given on the workshop in Waplewo 8–13 September 1997)

Cité par Sources :