Year: 2025
Type: preprint
Abstract: In this paper we complete the study of the Lan-Sheng-Zuo conjecture proposed in arXiv:1210.8280 for the curve case. Precisely, we prove that every semistable Higgs bundle is strongly semistable for curves of genus $g\leq 1$, and over any curves of genus $g\ge2$ construct explicit examples of semistable Higgs bundles of arbitrary big rank (the first example is $p=2,r=3$) which are not strongly semistable. These results are complementary to the strongly semistability theorem of Lan-Sheng-Yang-Zuo and Langer for semistable Higgs bundles of small rank.
Source: arXiv (Cornell University)
Authors: Liu, Bowen, Sheng, Mao
Institutions: Institute of Mathematical Sciences, Tsinghua University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6910745722
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