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


SIGMA 12 (2016), 007, 14 pages      arXiv:1508.06587      http://dx.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.

pdf (362 kb)   tex (18 kb)

References

  1. Atiyah M.F., Bott R., The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983), 523-615.
  2. Baraglia D., Classification of the automorphism and isometry groups of Higgs bundle moduli spaces, arXiv:1411.2228.
  3. Baraglia D., Schaposnik L.P., Higgs bundles and $(A,B,A)$-branes, Comm. Math. Phys. 331 (2014), 1271-1300, arXiv:1305.4638.
  4. Baraglia D., Schaposnik L.P., Real structures on moduli spaces of Higgs bundles, Adv. Theor. Math. Phys., to appear, arXiv:1309.1195.
  5. Brion M., Anti-affine algebraic groups, J. Algebra 321 (2009), 934-952, arXiv:0710.5211.
  6. Farkas H.M., Kra I., Riemann surfaces, Graduate Texts in Mathematics, Vol. 71, Springer-Verlag, New York - Berlin, 1980.
  7. Goldman W.M., The symplectic nature of fundamental groups of surfaces, Adv. Math. 54 (1984), 200-225.
  8. Griffiths P., Harris J., Principles of algebraic geometry, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1994.
  9. Kapustin A., Witten E., Electric-magnetic duality and the geometric Langlands program, Commun. Number Theory Phys. 1 (2007), 1-236, hep-th/0604151.
  10. Mazur B., Messing W., Universal extensions and one dimensional crystalline cohomology, Lecture Notes in Math., Vol. 370, Springer-Verlag, Berlin - New York, 1974.
  11. Mumford D., Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics, Vol. 5, Hindustan Book Agency, New Delhi, 2008.
  12. Simpson C.T., Moduli of representations of the fundamental group of a smooth projective variety. II, Inst. Hautes Études Sci. Publ. Math. (1994), 5-79.
  13. Weil A., Zum Beweis des Torellischen Satzes, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. IIa 1957 (1957), 33-53.

Previous article  Next article   Contents of Volume 12 (2016)