Compactifications of reductive groups as moduli stacks of bundles

Details Compactifications of reductive groups as moduli stacks of bundles Compactifications of reductive groups as moduli stacks of bundles

2011-05-24

arxiv.org/abs/1105.4830v1

Mathematics

Algebraic Geometry

35 pages

Scientific paper

Let G be a 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 connection with the spaces of weighted pointed curves studied by Losev-Manin.

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