Singular principal bundles over higher dimensional manifolds and their moduli spaces

Details Singular principal bundles over higher dimensional manifolds and their moduli spaces Singular principal bundles over higher dimensional manifolds and their moduli spaces

2002-01-10

arxiv.org/abs/math/0201085v1

IMRN 2002:23 (2002) 1183-1209. PII S1073792802107069

Mathematics

Algebraic Geometry

To appear in the International Mathematics Research Notices (IMRN), 20 pages

Scientific paper

In this note, we introduce the notion of a singular principal G-bundle, associated to a reductive algebraic group G over the complex numbers by means of a faithful representation $\varrho^\p\colon G\lra \SL(V)$. This concept is meant to provide an analogon to the notion of a torsion free sheaf as a generalization of the notion of a vector bundle. We will construct moduli spaces for these singular principal bundles which compactify the moduli spaces of stable principal bundles.

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