{"paper":{"title":"Stability of syzygy bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Pedro Macias Marques, Rosa Mar\\'ia Mir\\'o-Roig","submitted_at":"2010-08-16T18:32:34Z","abstract_excerpt":"We show that given integers $N$, $d$ and $n$ such that ${N\\ge2}$, ${(N,d,n)\\ne(2,2,5)}$, and ${N+1\\le n\\le\\tbinom{d+N}{N}}$, there is a family of $n$ monomials in $K[X_0,\\ldots,X_N]$ of degree $d$ such that their syzygy bundle is stable. Case ${N\\ge3}$ was obtained independently by Coand\\v{a} with a different choice of families of monomials [Coa09].\n  For ${(N,d,n)=(2,2,5)}$, there are $5$ monomials of degree~$2$ in $K[X_0,X_1,X_2]$ such that their syzygy bundle is semistable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2733","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"}