Resolutions of homogeneous bundles on 2

Giorgio Ottaviani[1]; Elena Rubei

  • [1] Dipartimento di Matematica ``U.Dini'', Viale Morgagni 67/A, c.a.p., 50134 Firenze (Italy)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 3, page 973-1015
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Ottaviani, Giorgio, and Rubei, Elena. "Resolutions of homogeneous bundles on ${\mathbb {P}}^2$." Annales de l’institut Fourier 55.3 (2005): 973-1015. <http://eudml.org/doc/116213>.

@article{Ottaviani2005,
abstract = {We characterize minimal free resolutions of homogeneous bundles on $\{\mathbb \{P\}\}^2$. Besides we study stability and simplicity of homogeneous bundles on $\{\mathbb \{P\}\}^2$ 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.},
affiliation = {Dipartimento di Matematica ``U.Dini'', Viale Morgagni 67/A, c.a.p., 50134 Firenze (Italy)},
author = {Ottaviani, Giorgio, Rubei, Elena},
journal = {Annales de l’institut Fourier},
keywords = {homogeneous bundles; minimal resolutions; quivers},
language = {eng},
number = {3},
pages = {973-1015},
publisher = {Association des Annales de l'Institut Fourier},
title = {Resolutions of homogeneous bundles on $\{\mathbb \{P\}\}^2$},
url = {http://eudml.org/doc/116213},
volume = {55},
year = {2005},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 3
SP - 973
EP - 1015
AB - We characterize minimal free resolutions of homogeneous bundles on ${\mathbb {P}}^2$. Besides we study stability and simplicity of homogeneous bundles on ${\mathbb {P}}^2$ 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.
LA - eng
KW - homogeneous bundles; minimal resolutions; quivers
UR - http://eudml.org/doc/116213
ER -

References

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  1. E. Ballico, On the stability of certain higher rank bundles on n , Rend. Circ. Mat. Palermo 41 (1992), 309-314 Zbl0770.14009MR1196622
  2. A.I. Bondal, M.M. Kapranov, Homogeneous Bundles, Seminar Rudakov, Helices and Vector bundles 148 (1990), 45-55, Cambridge University Press Zbl0742.14011
  3. J.-M. Drézet, J. Le Potier, Fibrés stables et fibrés exeptionnels sur le plan projectif, Ann. Sci. École Norm. Sup., 4e série 18 (1985), 193-244 Zbl0586.14007MR816365
  4. S. Faini, On the stability and simplicity of homogeneous bundles Zbl1178.14012
  5. W. Fulton, J. Harris, Representation Theory, A First Course,, (1991), Springer Verlag Zbl0744.22001MR1153249
  6. P. Gabriel, A.V. Roiter, Algebra VIII: Representations of finite dimensional algebras, 73 (1992), Springer Verlag Zbl0839.16001MR1239446
  7. L. Hille, Homogeneous vector bundles and Koszul algebras, Math. Nach. 191 (1998), 189-195 Zbl0957.14035MR1621314
  8. L. Hille, Small homogeneous vector bundles, (1994) Zbl0935.14009
  9. G. Horrocks, Vector bundles on the punctured spectrum of a local ring, Proc. London Math. Soc. 14 (1964), 689-713 Zbl0126.16801MR169877
  10. M.M. Kapranov, On the derived categories of coherent sheaves on some homogeneous spaces, Invent. Math. 92 (1988), 479-508 Zbl0651.18008MR939472
  11. A. King, Moduli of representations of finite-dimensional algebras, Quart. J. Math. Oxford Ser. (2) 45 (1994), 515-530 Zbl0837.16005MR1315461
  12. L. Migliorini, Stability of homogeneous bundles, Boll. Unione Mat. Ital. Sez. B 10 (1996), 963-990 Zbl0885.14024MR1430162
  13. G. Ottaviani, E. Rubei, Quivers and the cohomology of homogeneous vector bundles Zbl1100.14012
  14. S. Ramanan, Holomorphic vector bundles on homogeneous spaces, Topology 5 (1966), 159-177 Zbl0138.18602MR190947
  15. R. Rohmfeld, Stability of homogeneous vector bundles on P n , Geom. Dedicata 38 (1991), 159-166 Zbl0734.14004MR1104341
  16. D. Simpson, Linear representation of quivers 

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