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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Irreducible components of quiver Grassmannians
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by Andrew Hubery PDF
Trans. Amer. Math. Soc. 369 (2017), 1395-1458 Request permission

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.

References
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Additional Information
  • Andrew Hubery
  • Affiliation: Department of Mathematics, Bielefeld University, D-33501 Bielefeld, Germany
  • MR Author ID: 726430
  • Email: hubery@math.uni-bielefeld.de
  • 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
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 1395-1458
  • MSC (2010): Primary 16G20, 14M15
  • DOI: https://doi.org/10.1090/tran/6693
  • MathSciNet review: 3572278