We survey some parts of the vast literature on vector bundles on Hirzebruch surfaces, focusing on the rank-two case.
@article{bwmeta1.element.doi-10_2478_s11533-012-0046-2,
author = {Marian Aprodu and Vasile Br\^\i nz\u anescu and Marius Marchitan},
title = {Rank-two vector bundles on Hirzebruch surfaces},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1321-1330},
zbl = {1282.14071},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0046-2}
}
Marian Aprodu; Vasile Brînzănescu; Marius Marchitan. Rank-two vector bundles on Hirzebruch surfaces. Open Mathematics, Tome 10 (2012) pp. 1321-1330. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0046-2/
[1] Aprodu M., Brînzănescu V., Fibrés vectoriels de rang 2 sur les surfaces réglées, C. R. Math. Acad. Sci. Paris, 1996, 323(6), 627–630 | Zbl 0872.14036
[2] Aprodu M., Brînzănescu V., Stable rank-2 vector bundles over ruled surfaces, C. R. Math. Acad. Sci. Paris, 1997, 325(3), 295–300 http://dx.doi.org/10.1016/S0764-4442(97)83959-6 | Zbl 0905.14025
[3] Aprodu M., Brînzănescu V., Moduli spaces of vector bundles over ruled surfaces, Nagoya Math. J., 1999, 154, 111–122 | Zbl 0938.14024
[4] Aprodu M., Brînzănescu V., Beilinson type spectral sequences on scrolls, In: Moduli Spaces and Vector Bundles, Guanajuato, December, 2006, London Math. Soc. Lecture Note Ser., 359, Cambridge University Press, Cambridge, 2009, 426–436 http://dx.doi.org/10.1017/CBO9781139107037.014 | Zbl 1187.14051
[5] Aprodu M., Marchitan M., A note on vector bundles on Hirzebruch surfaces, C. R. Math. Acad. Sci. Paris, 2011, 349(11–12), 687–690 http://dx.doi.org/10.1016/j.crma.2011.04.013 | Zbl 1243.14033
[6] Brînzănescu V., Algebraic 2-vector bundles on ruled surfaces, Ann. Univ. Ferrara Sez. VII (N.S.), 1991, 37, 55–64 | Zbl 0795.14010
[7] Brînzănescu V., Holomorphic Vector Bundles over Compact Complex Surfaces, Lecture Notes in Math., 1624, Springer, Berlin, 1996
[8] Brînzănescu V., Stoia M., Topologically trivial algebraic 2-vector bundles on ruled surfaces. II, In: Algebraic Geometry, Bucharest, August 2–7, 1982, Lecture Notes in Math., 1056, Springer, Berlin, 1984, 34–46 http://dx.doi.org/10.1007/BFb0071768 | Zbl 0547.14006
[9] Brînzănescu V., Stoia M., Topologically trivial algebraic 2-vector bundles on ruled surfaces. I, Rev. Roumaine Math. Pures Appl., 1984, 29(8), 661–673 | Zbl 0547.14005
[10] Brosius J.E., Rank-2 vector bundles on a ruled surface. I, Math. Ann., 1983, 265(2), 155–168 http://dx.doi.org/10.1007/BF01460796 | Zbl 0503.55012
[11] Brosius J.E., Rank-2 vector bundles on a ruled surface. II, Math. Ann., 1983, 266(2), 199–214 http://dx.doi.org/10.1007/BF01458442 | Zbl 0509.14016
[12] Buchdahl N.P., Stable 2-bundles on Hirzebruch surfaces, Math. Z., 1987, 194(1), 143–152 http://dx.doi.org/10.1007/BF01168013 | Zbl 0627.14028
[13] Costa L., Miro-Ŕoig R.M., Rationality of moduli spaces of vector bundles on rational surfaces, Nagoya Math. J., 2002, 165, 43–69 | Zbl 1020.14012
[14] Friedman R., Algebraic Surfaces and Holomorphic Vector Bundles, Universitext, Springer, New York, 1998 http://dx.doi.org/10.1007/978-1-4612-1688-9
[15] Friedman R., Qin Z., On complex surfaces diffeomorphic to rational surfaces, Invent. Math., 1995, 120(1), 81–117 http://dx.doi.org/10.1007/BF01241123 | Zbl 0823.14022
[16] Fulger M., Marchitan M., Some splitting criteria on Hirzebruch surfaces, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 2011, 54(102)(4), 313–323 | Zbl 1274.14051
[17] Hoppe H.J., Spindler H., Modulräume stabiler 2-Bündel auf Regelflächen, Math. Ann., 1980, 249(2), 127–140 http://dx.doi.org/10.1007/BF01351410 | Zbl 0414.14018
[18] Marchitan M., Vector Bundles on Complex Varieties, PhD thesis, Institute of Mathematics of the Romanian Academy, 2011 (in Romanian)
[19] Marchitan M., Omalous bundles on Hirzebruch surfaces (in preparation) | Zbl 06522214
[20] Maruyama M., Stable vector bundles on an algebraic surface, Nagoya Math. J., 1975, 58, 25–68 | Zbl 0337.14026
[21] Okonek Chr., Schneider M., Spindler H., Vector Bundles on Complex Projective Spaces, Progr. Math., 3, Birkhäuser, Boston, 1980 | Zbl 0438.32016
[22] Pragacz P., Srinivas V., Pati V., Diagonal subschemes and vector bundles, Pure Appl. Math. Q., 2008, 4(4), 1233–1278 | Zbl 1157.14007
[23] Qin Z., Moduli spaces of stable rank-2 bundles on ruled surfaces, Invent. Math., 1992, 110(3), 615–626 http://dx.doi.org/10.1007/BF01231346 | Zbl 0808.14010
[24] Qin Z., Simple sheaves versus stable sheaves on algebraic surfaces, Math. Z., 1992, 209(4), 559–579 http://dx.doi.org/10.1007/BF02570854 | Zbl 0735.14014
[25] Qin Z., Equivalence classes of polarizations and moduli spaces of sheaves, J. Differential Geom., 1993, 37(2), 397–415 | Zbl 0802.14005
[26] Takemoto F., Stable vector bundles on algebraic surfaces, Nagoya Math. J., 1972, 47, 29–48 | Zbl 0245.14007
[27] Takemoto F., Stable vector bundles on algebraic surfaces. II, Nagoya Math. J., 1973, 52, 173–195 | Zbl 0296.14012
[28] Walter Ch., Irreducibility of moduli spaces of vector bundles on birationally ruled surfaces, In: Algebraic Geometry, Catania, September, 1993/Barcelona, September, 1994, Lecture Notes in Pure and Appl. Math., 200, Dekker, New York, 1998, 201–211