On very stablity of principal G-bundles

  • Hacen ZelaciEmail author
Original Paper


Let X be a smooth irreducible projective curve. In this note, we generalize the main result of Pauly and Peón-Nieto (Geometriae Dedicata 1–6, 2018) to principal G-bundles for any reductive linear algebraic group G. After defining very stability of principal G-bundles, we show that this definition is equivalent to the fact that the Hitchin fibration restricted to the space of Higgs fields on that principal bundle is finite. We also study the relation between very stability and other stability conditions in the case of \(\text {SL}_2\)-bundles.


Principal bundles Very stability Finiteness of the Hitchin map 

Mathematics Subject Classification (2010)

Primary 14H60 14H70 



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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Mathematical Institute of the University of BonnBonnGermany

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