Simple vector bundles on plane degenerations of an elliptic curve
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- by Lesya Bodnarchuk, Yuriy Drozd and Gert-Martin Greuel PDF
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Abstract:
In 1957 Atiyah classified simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classification by describing the simple vector bundles on all reduced plane cubic curves. Our main result states that a simple vector bundle on such a curve is completely determined by its rank, multidegree and determinant. Our approach, based on the representation theory of boxes, also yields an explicit description of the corresponding universal families of simple vector bundles.References
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Additional Information
- Lesya Bodnarchuk
- Affiliation: Max-Planck-Institut für Mathematik, Bonn, Germany
- Email: lesyabod@mpim-bonn.mpg.de
- Yuriy Drozd
- Affiliation: Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine
- MR Author ID: 211124
- Email: drozd@imath.kiev.ua
- Gert-Martin Greuel
- Affiliation: Fachbereich Mathematik, University of Kaiserslautern, Kaiserslautern, Germany
- MR Author ID: 76830
- Email: greuel@mathematik.uni-kl.de
- Received by editor(s): July 28, 2009
- Received by editor(s) in revised form: March 3, 2010
- Published electronically: August 25, 2011
- Additional Notes: We express our sincere thanks to Professor Serge Ovsienko for fruitful discussions and helpful advice. The first named author would like to thank Institut des Hautes Études Scientifiques and the Mathematisches Forschungsinstitut Oberwolfach, where she stayed during the period that this paper was written.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 137-174
- MSC (2000): Primary 16G60; Secondary 14H10, and, 14H60
- DOI: https://doi.org/10.1090/S0002-9947-2011-05354-7
- MathSciNet review: 2833580