{"paper":{"title":"The Gorenstein conjecture fails for the tautological ring of $\\mathcal{\\bar M}_{2,n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Petersen, Orsola Tommasi","submitted_at":"2012-10-21T20:28:19Z","abstract_excerpt":"Let $N$ be the smallest integer such that there is a non-tautological cohomology class of even degree on $\\mathcal{\\bar M}_{2,N}$. We remark that there is such a non-tautological class on $\\mathcal{\\bar M}_{2,20}$, by work of Graber and Pandharipande. We show that $\\mathcal{\\bar M}_{2,N}$ has non-tautological cohomology only in one degree, which is not the middle degree. In particular, it follows that the tautological ring of $\\mathcal{\\bar M}_{2,N}$ is not Gorenstein. We present some evidence suggesting that N=20 holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5761","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":""},"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"}