Geodesic
A remark on semistability of quiver bundles
Eurasian mathematical journal, Tome 3 (2012) no. 1, pp. 110-138.

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In this paper, we introduce a new semistability condition for quiver bundles which generalizes both the notion found by Álvarez-Cónsul and by the author. We construct moduli spaces for the semistable bundles, applying Geometric Invariant Theory. 
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A. Schmitt. A remark on semistability of quiver bundles. Eurasian mathematical journal, Tome 3 (2012) no. 1, pp. 110-138. http://geodesic.mathdoc.fr/item/EMJ_2012_3_1_a8/

[1] L. Álvarez-Cónsul, “Some results on the moduli spaces of quiver bundles”, Geom. Dedicata, 139 (2009), 99–120 | DOI | MR | Zbl

[2] L. Álvarez-Cónsul, O. García-Prada, “Hitchin–Kobayashi correspondence, quivers, and vortices”, Comm. Math. Phys., 238 (2003), 1–33 | MR | Zbl

[3] L. Álvarez-Cónsul, A. King, “A functorial construction of the moduli of sheaves”, Invent. Math., 168 (2007), 613–666 | DOI | MR | Zbl

[4] D. Banfield, “Stable pairs and principal bundles”, Q. J. Math., 51 (2000), 417–436 | DOI | MR | Zbl

[5] S. Bradlow, O. García-Prada, I. Mundet i Riera, “Relative Hitchin–Kobayashi correspondences for principal pairs”, Q. J. Math., 54 (2003), 171–220 | DOI | MR

[6] T.L. Gómez, A. Langer, A. Schmitt, I. Sols, “Moduli spaces for principal bundles in large characteristics”, Teichmüller theory and moduli problems, Ramanujan Mathematical Society Lecture Notes Series, 10, eds. I. Biswas et al., 2010, 281–371 | MR | Zbl

[7] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, 52, Springer-Verlag, New York–Heidelberg, 1977, xvi+496 pp. | DOI | MR | Zbl

[8] J. Heinloth, A. Schmitt, “The cohomology rings of moduli stacks of principal bundles over curves”, Documenta Math., 15 (2010), 423–488 | MR | Zbl

[9] F. Hirzebruch, Topological methods in algebraic geometry, translation from the German and appendix one by R. L. E. Schwarzenberger, appendix two by A. Borel, Classics in Mathematics, reprint of the 2nd, corr. print. of the 3rd ed. 1978, Springer-Verlag, Berlin, 1995, ix+234 pp. | MR | Zbl

[10] D. Huybrechts, M. Lehn, The geometry of moduli spaces of sheaves, 2nd ed., Cambridge University Press, Cambridge, 2010, xviii+325 pp. | MR | Zbl

[11] M. Lübke, A. Teleman, The universal Kobayashi–Hitchin correspondence on Hermitian manifolds, Mem. Amer. Math. Soc., 183, 2006, vi+97 pp. | MR

[12] A. Schmitt, “A universal construction for moduli spaces of decorated vector bundles over curves”, Transform. Groups, 9 (2004), 167–209 | DOI | MR | Zbl

[13] A. Schmitt, “Moduli for decorated tuples of sheaves and representation spaces for quivers”, Proc. Indian Acad. Sci., Math. Sci., 115 (2005), 15–49 | DOI | MR | Zbl

[14] A. Schmitt, Geometric invariant theory and decorated principal bundles, Zürich Lectures in Advanced Mathematics, European Mathematical Society, Zürich, vii+389 pp. | MR

[15] A. Sheshmani, Higher rank stable pairs and virtual localization, 87 pp., arXiv: 1011.6342v2 [math.AG] | MR | Zbl