Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 007, 14 pages      arXiv:1508.06587      https://doi.org/10.3842/SIGMA.2016.007

Automorphisms of ${\mathbb C}^*$ Moduli Spaces Associated to a Riemann Surface

David Baraglia a, Indranil Biswas b and Laura P. Schaposnik c
a) School of Mathematical Sciences, The University of Adelaide, Adelaide SA 5005, Australia
b) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
c) Department of Mathematics, University of Illinois, Chicago, IL 60607, USA

Received August 27, 2015, in final form January 15, 2016; Published online January 20, 2016

Abstract
We compute the automorphism groups of the Dolbeault, de Rham and Betti moduli spaces for the multiplicative group ${\mathbb C}^*$ associated to a compact connected Riemann surface.

Key words: holomorphic connection; Higgs bundle; character variety; automorphism.

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