Compactifications of reductive groups as moduli stacks of bundles. (18th August 2015)

• Record Type: Journal Article
• Authors: Martens, Johan; Thaddeus, Michael
• Is Part Of: Compositio mathematica. Volume 152:Number 1(2016:Jan.)
• Page Start: 62
• Page End: 98
• Publication Date: 2015-08-18
• Subjects: 14D23 (primary), -- 14H60, -- 14L30, -- 14M27, -- 20G15, -- 20M32 (secondary); reductive groups, -- compactifications, -- moduli problems, -- principal bundles; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X15007484
• Languages: English
• ISSNs: 0010-437X

Abstract

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 $GL_{n}$ .