Vector bundles on projective varieties and~representations of quivers
Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 217-249.

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We present equivalences between certain categories of vector bundles on projective varieties, namely cokernel bundles, Steiner bundles, syzygy bundles, and monads, and full subcategories of representations of certain quivers. As an application, we provide decomposability criteria for such bundles.
Keywords: vector bundles, representations of quivers.
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Marcos Jardim; Daniela Moura Prata. Vector bundles on projective varieties and~representations of quivers. Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 217-249. http://geodesic.mathdoc.fr/item/ADM_2015_20_2_a3/

[1] M. C. Brambilla, “Cokernel bundles and Fibonacci bundles”, Math. Nach., 281 (2008), 499–516 | DOI | MR | Zbl

[2] H. Brenner, “Looking out for stable syzygy bundles”, Adv. Math., 219 (2008), 401–427 | DOI | MR | Zbl

[3] I. Dolgachev, M. Kapranov, “Arrangements of hyperplanes and vector bundles on $\mathbb{P}^n$”, Duke Math. J., 71 (1993), 633–664 | DOI | MR | Zbl

[4] M. Jardim, V. M. F. Silva, “Decomposability criterion for linear sheaves”, Cent. Eur. J. Math., 10 (2012), 1292–1299 | DOI | MR | Zbl

[5] V. G. Kac, “Infinite root systems, representations of graphs and invariant theory”, Invent. Math., 56 (1980), 57–92 | DOI | MR | Zbl

[6] P. M. Marques, H. Soares, “Cohomological caracterisation of monads”, Math. Nachr., 287 (2014), 2057–2070 | DOI | MR | Zbl

[7] R. M. Miró-Roig, H. Soares, “Cohomological characterisation of Steiner bundles”, Forum Math., 21 (2009), 871–891 | MR | Zbl

[8] A. Schofield, “General representations of quivers”, Proc. London Math. Soc., 65 (1992), 46–64 | DOI | MR | Zbl

[9] A. Schofield, “Birational classification of moduli spaces of representations of quivers”, Indag. Mathem., 12 (2001), 407–432 | DOI | MR | Zbl

[10] H. Soares, Steiner vector bundles on algebraic varieties, Ph.D. Thesis, University of Barcelona, 2008