Mukai-Sakai bound for equivariant principal bundles

Usha N. Bhosle School of Mathematics, Tata Institute of Fundamental Research Indranil Biswas School of Mathematics, Tata Institute of Fundamental Research

TBD mathscidoc:1701.333049

Arkiv for Matematik, 43, (1), 133-141, 2003.5
Mukai and Sakai proved that given a vector bundle$E$of rank$n$on a connected smooth projective curve of genus$g$and any$r$∈[1,$n$], there is subbundle$S$of rank$r$such that deg Hom($S, E/S$)≤$r$($n−r$)$g$. We prove a generalization of this bound for equivariant principal bundles. Our proof even simplifies the one given by Holla and Narasimhan for usual principal bundles.
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@inproceedings{usha2003mukai-sakai,
  title={Mukai-Sakai bound for equivariant principal bundles},
  author={Usha N. Bhosle, and Indranil Biswas},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203613349677858},
  booktitle={Arkiv for Matematik},
  volume={43},
  number={1},
  pages={133-141},
  year={2003},
}
Usha N. Bhosle, and Indranil Biswas. Mukai-Sakai bound for equivariant principal bundles. 2003. Vol. 43. In Arkiv for Matematik. pp.133-141. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203613349677858.
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