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Compactifications of reductive groups as moduli stacks of bundles

Published online by Cambridge University Press:  18 August 2015

Johan Martens
Affiliation:
School of Mathematics and Maxwell Institute, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland email johan.martens@ed.ac.uk
Michael Thaddeus
Affiliation:
Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, USA email thaddeus@math.columbia.edu
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Abstract

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Let $G$ be a split reductive group. We introduce the moduli problem of bundle chains parametrizing framed principal $G$-bundles on chains of lines. Any fan supported in a Weyl chamber determines a stability condition on bundle chains. Its moduli stack provides an equivariant toroidal compactification of $G$. All toric orbifolds may be thus obtained. Moreover, we get a canonical compactification of any semisimple $G$, which agrees with the wonderful compactification in the adjoint case, but which in other cases is an orbifold. Finally, we describe the connections with Losev–Manin’s spaces of weighted pointed curves and with Kausz’s compactification of $GL_{n}$.

Type
Research Article
Copyright
© The Authors 2015 

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