{"paper":{"title":"On the canonical degree of a Gorenstein minimal threefold of general type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jiabin Du, Yong Hu","submitted_at":"2026-06-30T06:00:07Z","abstract_excerpt":"Let $X$ be a Gorenstein minimal $3$-fold of general type whose canonical map is generically finite. We prove that if $p_g(X)> 243$, then the degree of the canonical map is at most $72$. Moreover, equality holds only if the general fibre $F$ of the Albanese morphism of $X$ is a smooth minimal surface of general type satisfying $p_g(F)=3,q(F)=0$ and $K_F^2=36$, and the canonical map of $F$ has degree $36$. This result improves the lower bound on $p_g(X)$ previously obtained by Jin-Xing Cai~\\cite{Cai08}.\n  As a consequence, we show that if the canonical degree is bigger than $64$, then the genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31170","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/2606.31170/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"}