{"paper":{"title":"Spinor modifications of conic bundles and derived categories of 1-nodal Fano threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander Kuznetsov","submitted_at":"2025-02-04T08:04:22Z","abstract_excerpt":"Given a flat conic bundle $X/S$ and an abstract spinor bundle $\\mathcal{F}$ on $X$ we define a new conic bundle $X_{\\mathcal{F}}/S$, called a spinor modification of $X$, such that the even Clifford algebras of $X/S$ and $X_{\\mathcal{F}}/S$ are Morita equivalent and the orthogonal complements of $\\mathrm{D}^{\\mathrm{b}}(S)$ in $\\mathrm{D}^{\\mathrm{b}}(X)$ and $\\mathrm{D}^{\\mathrm{b}}(X_{\\mathcal{F}})$ are equivalent as well. We demonstrate how the technique of spinor modifications works in the example of conic bundles associated with some nonfactorial 1-nodal prime Fano threefolds. In particula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02082","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/2502.02082/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"}