{"paper":{"title":"Linear subspaces of the intersection of two quadrics via Kuznetsov component","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shizhuo Zhang, Yanjie Li","submitted_at":"2024-01-01T06:13:30Z","abstract_excerpt":"Let $Q_i(i=1,2)$ be $2g$ dimensional quadrics in $\\mathbb{P}^{2g+1}$ and let $Y$ be the smooth intersection $Q_1\\cap Q_2$. We associate the linear subspace in $Y$ with vector bundles on the hyperelliptic curve $C$ of genus $g$ by the left adjoint functor of $\\Phi:D^b(C)\\rightarrow D^b(Y)$. As an application, we give a different proof of the classification of line bundles and stable bundles of rank $2$ on hyperelliptic curves given by Desale and Ramanan. When $g=3$, we show that the projection functor induces a closed embedding $\\alpha:Y\\rightarrow SU^s_C(4,h)$ into the moduli space of stable b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.00677","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.00677/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"}