Geometriae Dedicata

, Volume 179, Issue 1, pp 187–195 | Cite as

Symplectic form on hyperpolygon spaces

  • Indranil Biswas
  • Carlos Florentino
  • Leonor Godinho
  • Alessia Mandini
Original paper
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Abstract

In Godinho and Mandini (Adv Math 244:465–532, 2013), a family of parabolic Higgs bundles on \({{\mathbb {C}}}{\mathbb {P}}^1\) was constructed and the parameter space for the family was identified with a moduli space of hyperpolygons. Our aim here is to give a canonical alternative construction of this family. This enables us to compute the Higgs symplectic form for this family and show that the isomorphism of Godinho and Mandini (Adv Math 244:465–532, 2013) is actually a symplectomorphism.

Keywords

Hyperpolygon space Parabolic Higgs bundles Symplectic form  Liouville form 

Mathematics Subject Classification (2000)

14D20 14H60 
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Notes

Acknowledgments

We thank the referee for helpful comments. The first author wishes to thank Instituto Superior Técnico, where the work was carried out, for its hospitality; his visit to IST was funded by the FCT project PTDC/MAT/099275/2008. He also acknowledges the support of J. C. Bose Fellowship. This work was partially supported by the FCT projects PTDC/MAT/108921/2008, PTDC/MAT/120411/2010 and the FCT Grant SFRH/BPD/44041/2008.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Indranil Biswas
    • 1
  • Carlos Florentino
    • 2
  • Leonor Godinho
    • 2
  • Alessia Mandini
    • 3
  1. 1.School of MathematicsTata Institute of Fundamental ResearchBombayIndia
  2. 2.Departamento Matemática, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal
  3. 3.Departamento de MatemáticaPUC–RioRio de JaneiroBrasil

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