{"paper":{"title":"Stability and moduli spaces of syzygy bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Pedro Macias Marques","submitted_at":"2009-09-25T10:05:31Z","abstract_excerpt":"It is a longstanding problem in Algebraic Geometry to determine whether the syzygy bundle $E_{d_1,...,d_n}$ on $\\mathbb{P}^N$ defined as the kernel of a general epimorphism \\[\\phi:\\mathcal{O}(-d_1)\\oplus...\\oplus\\mathcal{O}(-d_n) \\to\\mathcal{O}\\] is (semi)stable. In this thesis, attention is restricted to the case of syzygy bundles $\\mathrm{Syz}(f_1,...,f_n)$ on $\\mathbb{P}^N$ associated to $n$ generic forms $f_1,...,f_n\\in K[X_0,...,X_N]$ of the same degree $d$, for ${N\\ge2}$.\n  The first goal is to prove that $\\mathrm{Syz}(f_1,...,f_n)$ is stable if \\[N+1\\le n\\le\\tbinom{d+N}{N},\\] except for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4646","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0909.4646/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}