{"paper":{"title":"Metha-Ramanathan for {\\epsilon} and k-semistable Decorated Sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrea Pustetto","submitted_at":"2013-12-27T18:51:07Z","abstract_excerpt":"This paper is devoted to generalizing the Mehta-Ramanathan restriction theorem to the case of {\\epsilon}-semistable and k-semistable decorated sheaves. After recalling the definition of decorated sheaves and their usual semistability we define the {\\epsilon} and k-(semi)stablility. We first prove the existence of a (unique) {\\epsilon}-maximal destabilizing subsheaf for decorated sheaves (Section 3.1). After some others preliminar results (such as the opennes condition for families of {\\epsilon}-semistable decorated sheaves) we finally prove, in Section 3.7, a restriction theorem for slope {\\ep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7312","kind":"arxiv","version":1},"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"}