{"paper":{"title":"Semistable rank 2 sheaves with singularities of mixed dimension on $\\mathbb{P}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander S. Tikhomirov, Alexey N. Ivanov","submitted_at":"2017-03-15T00:32:02Z","abstract_excerpt":"We describe new irreducible components of the Gieseker-Maruyama moduli scheme $\\mathcal{M}(3)$ of semistable rank 2 coherent sheaves with Chern classes $c_1=0,\\ c_2=3,\\ c_3=0$ on $\\mathbb{P}^3$, general points of which correspond to sheaves whose singular loci contain components of dimensions both 0 and 1. These sheaves are produced by elementary transformations of stable reflexive rank 2 sheaves with $c_1=0,\\ c_2=2,\\ c_3=2$ or 4 along a disjoint union of a projective line and a collection of points in $\\mathbb{P}^3$. The constructed families of sheaves provide first examples of irreducible co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04851","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"}