ON A CONJECTURE OF LAN–SHENG–ZUO ON SEMISTABLE HIGGS BUNDLES: RANK 3 CASE

@inproceedings{Li2014ONAC,
  title={ON A CONJECTURE OF LAN–SHENG–ZUO ON SEMISTABLE HIGGS BUNDLES: RANK 3 CASE},
  author={Lingguang Li},
  year={2014}
}
Let X be a smooth projective curve of genus g over an algebraically closed field k of characteristic p > 2. We prove that any rank 3 nilpotent semistable Higgs bundle (E, θ) on X is a strongly semistable Higgs bundle. This gives a partially affirmative answer to a conjecture of Lan–Sheng–Zuo [Semistable Higgs bundles and representations of algebraic fundamental groups: positive characteristic case, preprint (2012), arXiv:1210.8280][(Very recently, A. Langer [Semistable modules over Lie… CONTINUE READING