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Tame and Wild Projective Curves and Classification of Vector Bundles

✍ Scribed by Yuri A Drozd; Gert-Martin Greuel

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 363 KB
Volume: 246
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8934

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✦ Synopsis

We propose a new method of classifying vector bundles on projective curves, especially singular ones, according to their "representation type." In particular, we prove that the classification problem of vector bundles, respectively of torsion-free sheaves, on projective curves is always finite, tame, or wild. We completely classify curves which are of finite, respectively tame, vector bundle type by their dual graph. Moreover, our methods yield a geometric description of all indecomposable vector bundles and torsion-free sheaves on finite and tame curves.

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