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Compactifications of reductive groups as moduli stacks of bundles
- Part of
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- Journal:
- Compositio Mathematica / Volume 152 / Issue 1 / January 2016
- Published online by Cambridge University Press:
- 18 August 2015, pp. 62-98
- Print publication:
- January 2016
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- Article
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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 
$GL_{n}$.
