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Type: Journal article
Title: Classification of the automorphism and isometry groups of Higgs bundle moduli spaces
Author: Baraglia, D.
Citation: Proceedings of the London Mathematical Society, 2016; 112(5):827-854
Publisher: Oxford University Press
Issue Date: 2016
ISSN: 0024-6115
Statement of
David Baraglia
Abstract: Let Mn,d be the moduli space of semi-stable rank n, trace-free Higgs bundles with fixed determinant of degree d on a Riemann surface of genus at least 3. We determine the following automorphism groups of Mn,d: (i) the group of automorphisms as a complex analytic variety, (ii) the group of holomorphic symplectomorphisms, (iii) the group of Kähler isomorphisms, (iv) the group of hypercomplex automorphisms, (v) the group ofhyper-Kähler isomorphisms. When n and d are coprime we show that Mn,d admits an anti-holomorphic isomorphism if and only if the corresponding Riemann surface admits such a map. We then use this to determine the isometry group of Mn,d.
Rights: © 2016 London Mathematical Society
DOI: 10.1112/plms/pdw014
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Mathematical Sciences publications

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