{"paper":{"title":"Stability and Unobstructedness of Syzygy Bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"L. Costa, P. Macias Marques, R.M. Mir\\'o-Roig","submitted_at":"2009-01-16T11:03:56Z","abstract_excerpt":"It is a longstanding problem in Algebraic Geometry to determine whether the syzygy bundle $E_{d_1,..., d_n}$ on $\\PP^N$ defined as the kernel of a general epimorphism $\\xymatrix{\\phi:\\cO(-d_1)\\oplus...\\oplus\\cO(-d_n)\\ar[r] &\\cO}$ is (semi)stable. In this note, we restrict our attention to the case of syzygy bundles $E_{d,n}$ on $\\PP^N$ associated to $n$ generic forms $f_1,...,f_n\\in K[X_0,X_1,..., X_N]$ of the same degree $d$. Our first goal is to prove that $E_{d,n}$ is stable if $N+1\\le n\\le\\tbinom{d+2}{2}+N-2$. This bound improves, in general, the bound $n\\le d(N+1)$ given by G. Hein in \\ci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.2457","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"}