{"paper":{"title":"The polarized degree of irrationality of $K3$ surfaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Federico Moretti","submitted_at":"2023-03-13T17:09:09Z","abstract_excerpt":"Given a polarized variety $(X,L)$, we construct and study projections of low degree $ X\\dashrightarrow \\mathbb{P}(H^0(L^\\vee)) \\dashrightarrow \\mathbb P ^n $ using the associated kernel bundles. As an application, we can show that the degree of irrationality of a very general $(1,6)$ abelian surface, as well as that of a very general $K3$ surface of genus $6$ is $3$. We also give new upper bounds for $K3$ surfaces of any genus. Moreover, in the case of surfaces, this observation can be used to show that maps of the degree at most $d$ move in families. We study the family of projections of mini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.07289","kind":"arxiv","version":4},"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/2303.07289/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"}