{"paper":{"title":"On a Conjecture of Lan-Sheng-Zuo on Semistable Higgs Bundles: Rank 3 Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lingguang Li","submitted_at":"2013-06-16T14:47:46Z","abstract_excerpt":"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 $(E,\\theta)$ on $X$ is a strongly semistable Higgs bundle. This gives a partially affirmative answer to a conjecture of Lan-Sheng-Zuo \\cite{LanShengZuo12ii}\\footnotemark[1]. In addition, we prove a tensor product theorem for strongly semistable Higgs bundles with $p$ satisfying some bounds (Theorem \\ref{TensorTheorem}). From this we reprove a tensor theorem for semistable Higgs bundles on the condition that the Lan-Sheng-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3666","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}