A closer look at semistability for singular principal bundles

2004/05/31 by Alexander H. W. Schmitt
Mathematics · #math.AG

paper · pdf · doi:10.1155/s1073792804132984

published as IMRN 2004:62 (2004) 3327-3366 · To appear in the International Mathematics Research Notices. V2: Minor corrections

arxiv created 2004/07/27 · arxiv updated 2009/12/01

Abstract

We substantially refine the theory of singular principal bundles introduced in a former paper. In particular, we show that we need only honest singular principal bundles in our compactification. These are objects which carry the structure of a rational principal bundle in the sense of Ramanathan. Moreover, we arrive at a much simpler semistability condition. In the case of a semisimple group, this is just the Gieseker-version of Ramanathan's semistability condition for the corresponding rational principal G-bundle.

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