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Communications in Mathematical Physics

, Volume 367, Issue 1, pp 127–150 | Cite as

Asymptotics of Hitchin’s Metric on the Hitchin Section

  • David DumasEmail author
  • Andrew Neitzke
Article

Abstract

We consider Hitchin’s hyperkähler metric g on the moduli space \({\mathcal{M}}\) of degree zero SL(2)-Higgs bundles over a compact Riemann surface. It has been conjectured that, when one goes to infinity along a generic ray in \({\mathcal{M}}\), g converges to an explicit “semiflat” metric gsf, with an exponential rate of convergence.We show that this is indeed the case for the restriction of g to the tangent bundle of the Hitchin section \({\mathcal{B} \subset \mathcal{M}}\).

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Notes

Acknowledgements

The authors thank Rafe Mazzeo, Jan Swoboda, Hartmut Weiss, and Michael Wolf for helpful discussions related to this work, and also thank the anonymous referee for a careful reading and helpful comments and corrections. The authors also gratefully acknowledge support from the U.S. National Science Foundation through individual Grants DMS 1709877 (DD), DMS 1711692 (AN), and through the GEAR Network (DMS 1107452, 1107263, 1107367, “RNMS: GEometric structures And Representation varieties”) which supported a conference where some of this work was conducted.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics, and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  2. 2.Department of MathematicsUniversity of Texas at AustinAustinUSA

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