Simple vector bundles on plane degenerations of an elliptic curve
Algebraic Geometry
2010-03-26 v2 Representation Theory
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.
Keywords
Cite
@article{arxiv.0903.4966,
title = {Simple vector bundles on plane degenerations of an elliptic curve},
author = {Lesya Bodnarchuk and Yuriy Drozd and Gert-Martin Greuel},
journal= {arXiv preprint arXiv:0903.4966},
year = {2010}
}