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arXiv · 1407.2293

The geometry of uniserial representations of algebras II. Alternate viewpoints and uniqueness

Klaus Bongartz·Birge Huisgen-Zimmermann
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Abstract

We provide two alternate settings for a family of varieties modeling the uniserial representations with fixed sequence of composition factors over a finite dimensional algebra. The first is a quasi-projective subvariety of a Grassmannian containing the members of the mentioned family as a principal affine open cover; among other benefits, one derives invariance from this intrinsic description. The second viewpoint re-interprets the `uniserial varieties' as locally closed subvarieties of the traditional module varieties; in particular, it exhibits closedness of the fibres of the canonical maps from the uniserial varieties to the uniserial representations.

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Klaus Bongartz, Birge Huisgen-Zimmermann. 2014-07-08. The geometry of uniserial representations of algebras II. Alternate viewpoints and uniqueness. https://arxiv.org/abs/1407.2293

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