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Irreducible components of quiver Grassmannians


Author: Andrew Hubery
Journal: Trans. Amer. Math. Soc. 369 (2017), 1395-1458
MSC (2010): Primary 16G20, 14M15
DOI: https://doi.org/10.1090/tran/6693
Published electronically: May 17, 2016
MathSciNet review: 3572278
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Abstract: We consider the action of a smooth, connected group scheme $ G$ on a scheme $ Y$, and discuss the problem of when the saturation map $ \Theta \colon G\times X\to Y$ is separable, where $ X\subset Y$ is an irreducible subscheme. We provide sufficient conditions for this in terms of the induced map on the fibres of the conormal bundles to the orbits. Using jet space calculations, one then obtains a criterion for when the scheme-theoretic image of $ \Theta $ is an irreducible component of $ Y$.

We apply this result to Grassmannians of submodules and several other schemes arising from representations of algebras, thus obtaining a decomposition theorem for their irreducible components in the spirit of the result by Crawley-Boevey and Schröer for module varieties.


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Additional Information

Andrew Hubery
Affiliation: Department of Mathematics, Bielefeld University, D-33501 Bielefeld, Germany
Email: hubery@math.uni-bielefeld.de

DOI: https://doi.org/10.1090/tran/6693
Received by editor(s): September 10, 2013
Received by editor(s) in revised form: January 20, 2015, and February 19, 2015
Published electronically: May 17, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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