Moduli of vector bundles on higher-dimensional base manifolds - Construction and Variation

Abstract

We survey recent progress in the study of moduli of vector bundles on higher-dimensional base manifolds. In particular, we discuss an algebro-geometric construction of an analogue for the Donaldson-Uhlenbeck compactification and explain how to use moduli spaces of quiver representations to show that Gieseker-Maruyama moduli spaces with respect to two different chosen polarisations are related via Thaddeus-flips through other "multi-Gieseker"-moduli spaces of sheaves. Moreover, as a new result, we show the existence of a natural morphism from a multi-Gieseker moduli space to the corresponding Donaldson-Uhlenbeck moduli space.

21 pages; v2: minor changes as requested by referee, added Remark 4.7 concerning Compactified Jacobians; to appear in the proceedings of VBAC 2014 "Algebraic Varieties: Bundles, Topology, Physics"

References in corpus (1)

• A functorial construction of moduli of sheaves

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• Moduli spaces of slope-semistable sheaves with reflexive Seshadri graduations
• Continuity of HYM connections with respect to metric variations