Mathematics – Algebraic Geometry
Scientific paper
2001-02-22
Rev. Roumaine Math. Pures Appl. 45 (2000), 681-711
Mathematics
Algebraic Geometry
To appear in the Revue roumaine de math'ematiques pures et appliq'ees
Scientific paper
We provide a construction of the moduli spaces of framed Hitchin pairs and their master spaces. These objects have come to interest as algebraic versions of solutions of certain coupled vortex equations by work of Lin and Stupariu. Our method unifies and generalizes constructions of several similar moduli spaces. Here are some points which are also of interest in other similar situations: - Our construction does not require the symmetricity condition that the map ^2G x E -> E be zero, usually appearing in the context of Higgs bundles. - We carry out a detailed analysis of the polynomial stability parameter without referring to GIT. This sheds some light on intrinsic properties of such parameter dependent stability concepts. - The construction corrects an inaccuracy in our previous construction of the compactification of the Hitchin space and generalizes it.
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