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Branes and moduli spaces of Higgs bundles on smooth projective varieties

Abstract

Given a smooth complex projective variety M and a smooth closed curve \(X\, \subset \, M\) such that the homomorphism of fundamental groups \(\pi _1(X)\, \longrightarrow \, \pi _1(M)\) is surjective, we study the restriction map of Higgs bundles, namely from the Higgs bundles on M to those on X. In particular, we investigate the interplay between this restriction map and various types of branes contained in the moduli spaces of Higgs bundles on M and X. We also consider the setup where a finite group is acting on M via holomorphic automorphisms or anti-holomorphic involutions, and the curve X is preserved by this action. Branes are studied in this context.

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Acknowledgements

We thank the two referees for going through the paper very carefully. IB is supported by a J. C. Bose Fellowship. LPS is partially supported by NSF CAREER Award DMS-1749013. On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Correspondence to Indranil Biswas.

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Biswas, I., Heller, S. & Schaposnik, L.P. Branes and moduli spaces of Higgs bundles on smooth projective varieties. Res Math Sci 8, 52 (2021). https://doi.org/10.1007/s40687-021-00286-z

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Keywords

  • Branes
  • Connection
  • Higgs bundle
  • HyperKähler manifold
  • Twistor space

Mathematics Subject Classification

  • 14D21
  • 32L25
  • 14H70