{"paper":{"title":"Reachable sheaves on ribbons and deformations of moduli spaces of sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jean-Marc Drezet","submitted_at":"2016-02-20T09:20:27Z","abstract_excerpt":"A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that C=Y_red is smooth. In this case, L=I_C/I_C^2 is a line bundle on C. If Y is of multiplicity 2, i.e. if I_C^2=0, Y is called a ribbon. If Y is a ribbon and h^0(L^{-2})>0, then Y can be deformed to smooth curves, but in general a coherent sheaf on Y cannot be deformed in coherent sheaves on the smooth curves.\n  A ribbon with associated line bundle L such that deg(L)=-d<0 can be deformed to reduced curves having 2 irreducible components if L can be written "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06386","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"}