Simple vector bundles on plane degenerations of an elliptic curve
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Date
2009
Volume
2009-20
Issue
Journal
Series Titel
Oberwolfach Preprints (OWP)
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Publisher
Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach
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Abstract
In 1957 Atiyah classifed simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classifcation 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.
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This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.