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arXiv · 1503.00319

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

Daniel Greb·Julius Ross·Matei Toma
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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.

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Daniel Greb, Julius Ross, Matei Toma. 2015-08-20. Moduli of vector bundles on higher-dimensional base manifolds - Construction and Variation. https://doi.org/10.1142/s0129167x16500543

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