no. 3
Resolutions of homogeneous bundles on ℙ 2
[Résolutions des fibrés homogènes sur ℙ 2 .]
Ottaviani, Giorgio1 ; Rubei, Elena
1 Dipartimento di Matematica ``U.Dini'', Viale Morgagni 67/A, c.a.p., 50134 Firenze (Italy)
Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 973-1015.

Nous caractérisons les résolutions libres minimales des fibrés homogènes sur ℙ 2 et nous étudions la stabilité et la simplicité des fibrés homogènes sur ℙ 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 ℙ 2 . Besides we study stability and simplicity of homogeneous bundles on ℙ 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) 
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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://www.numdam.org/articles/10.5802/aif.2119/

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