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.
Keywords
Cite
@article{arxiv.1503.00319,
title = {Moduli of vector bundles on higher-dimensional base manifolds - Construction and Variation},
author = {Daniel Greb and Julius Ross and Matei Toma},
journal= {arXiv preprint arXiv:1503.00319},
year = {2018}
}
Comments
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"