{"paper":{"title":"Instability of Truncated Symmetric Powers of sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fei Yu, Lingguang Li","submitted_at":"2010-10-20T15:22:05Z","abstract_excerpt":"Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$. Let $F_X:X\\rightarrow X$ be the absolute Frobenius morphism, and $\\E$ a torsion free sheaf on $X$. We give a upper bound of instability of truncated symmetric powers $\\mathrm{T}^l(\\E)(0\\leq l\\leq\\rk(\\E)(p-1))$ in terms of $L_{\\max}(\\Omg^1_X)$, $\\mathrm{I}(\\Omg^1_X)$ and $\\mathrm{I}(\\E)$ (Theorem \\ref{InstabTl}). As an application, We obtain a upper bound of Frobenius direct image ${F_X}_*(\\E)$ and some sufficient conditions of slope semi-stability of ${F_X}_*(\\E)$. In additio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4228","kind":"arxiv","version":3},"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"}