{"paper":{"title":"Jacobian algebras and variation of hyperplane sections","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abbas Nasrollah Nejad, Giovanna Ilardi, Saeed Tafazolian","submitted_at":"2026-06-21T16:49:57Z","abstract_excerpt":"We study the variation in moduli of hyperplane sections of a hypersurface $V(f)\\subseteq \\mathbf P^n$ with at most isolated singularities. Using the Milnor algebra $M(f)$, we give an infinitesimal quotient criterion for the hyperplane-section map $\\Phi(f):(\\mathbf P^n)^*\\dashrightarrow M(d,n-1)$ to be generically finite onto its image. The passage from the infinitesimal quotient to the coarse moduli space is justified by a local GIT slice argument. Our approach gives a Jacobian-algebraic extension of the Beauville--Patel--Riedl--Tseng theory from smooth hypersurfaces to hypersurfaces with isol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22587","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/2606.22587/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"}