We give a complete classification of stable vector bundles over a cuspidal cubic and calculate their cohomologies. The technique of matrix problems is used, similar to [2, 3].
@article{bwmeta1.element.doi-10_2478_BF02475185,
author = {Lesya Bodnarchuk and Yuriy Drozd},
title = {Stable vector bundles over cuspidal cubics},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {650-660},
zbl = {1040.14018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475185}
}
Lesya Bodnarchuk; Yuriy Drozd. Stable vector bundles over cuspidal cubics. Open Mathematics, Tome 1 (2003) pp. 650-660. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475185/
[1] I. Burban: “Stable vector bundles on a rational curve with one node”, Ukrainian Math. J., Vol. 55, No. 5, (2000).
[2] Y. Drozd: “Matrix problems, small reduction and representations of a class of mixed Lie groups”, In: Representations of Algebras and Related Topics, Cambridge Univ. Press, 1992, pp. 225–249. | Zbl 0829.16009
[3] Y. Drozd and G.-M. Greuel: “Tame and wild projective curves and classification of vector bundles”, J. Algebra, Vol. 246, (2001), pp. 1–54. http://dx.doi.org/10.1006/jabr.2001.8934
[4] A. Grothendieck: “Sur la classification des fibrés holomorphes sur la sphère de Riemann”, Amer. J. Math., Vol. 79, (1956), pp. 121–138. http://dx.doi.org/10.2307/2372388 | Zbl 0079.17001
[5] R. Hartshorn: Algebraic Geometry, Springer, New York, 1977.
[6] C. S. Seshadri: “Fibrés vectoriels sur les courbes algébriques”, Astérisque, Vol. 96, (1982). | Zbl 0517.14008