I would like to ask if someone knows good references for the construction of the moduli space of Higgs bundles from the G.I.T point of view, and the study of this moduli space from the stacky point of view.
Thank you for your time.
2026-02-22 23:34:23.1771803263
References for Higgs bundles
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The first GIT construction of the moduli space of semistable Higgs bundles on a curve is due to Nitsure, and is described in detail in his paper "Moduli space of semistable pairs on a curve" (https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/s3-62.2.275).
As for the moduli stack of Higgs bundles, its construction is given in the lectures notes "An introduction to moduli stacks, with a view towards Higgs bundles" by Casalaina-Martin and Wise (https://arxiv.org/pdf/1708.08124.pdf). There is also a comparison of the moduli stack and moduli space of semistable Higgs bundles in Section 7.7 of these notes.