Simple vector bundles on plane degenerations of an elliptic curve

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Date
2009-03-13MFO Scientific Program
Research in Pairs 2009Series
Oberwolfach Preprints;2009,20Author
Bodnarchuk, Lesya
Drozd, Jurij A.
Greuel, Gert-Martin
Metadata
Show full item recordOWP-2009-20
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.