Compactifications of reductive groups as moduli stacks of bundles

Abstract

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).

42 pages; section on functoriality added, numerous other improvements requested by referee, numbering changed accordingly; to appear in Compositio Mathematica

References in corpus (5)

• On the wonderful compactification
• Moduli of Singular Curves
• Variations on a theme of Grothendieck
• A relative Hilbert-Mumford criterion
• On the Chow ring of the stack of rational nodal curves

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• The wonderful compactification for quantum groups
• Rota-Baxter algebras, singular hypersurfaces, and renormalization on Kausz compactifications
• Group Compactifications and Moduli Spaces
• Canonical blow-ups of Grassmann manifolds