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In 1957 Atiyah classified simple and indecomposable vector bundles on anelliptic curve. In this article we generalize his classification by describingthe simple vector bundles on all reduced plane cubic curves. Our main resultstates that a simple vector bundle on such a curve is completely determined byits rank, multidegree and determinant. Our approach, based on therepresentation theory of boxes, also yields an explicit description of thecorresponding universal families of simple vector bundles.

Simple vector bundles on plane degenerations of an elliptic curve