{"paper":{"title":"Positivity of Riemann-Roch polynomials and Todd classes of hyperk\\\"{a}hler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Chen Jiang","submitted_at":"2020-08-11T13:11:39Z","abstract_excerpt":"For a hyperk\\\"{a}hler manifold $X$ of dimension $2n$, Huybrechts showed that there are constants $a_0, a_2, \\dots, a_{2n}$ such that $$\\chi(L) =\\sum_{i=0}^n\\frac{a_{2i}}{(2i)!}q_X(c_1(L))^{i}$$ for any line bundle $L$ on $X$, where $q_X$ is the Beauville-Bogomolov-Fujiki quadratic form of $X$. Here the polynomial $\\sum_{i=0}^n\\frac{a_{2i}}{(2i)!}q^{i}$ is called the Riemann-Roch polynomial of $X$.\n  In this paper, we show that all coefficients of the Riemann-Roch polynomial of $X$ are positive. This confirms a conjecture proposed by Cao and the author, which implies Kawamata's effective non-va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.04685","kind":"arxiv","version":3},"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/2008.04685/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"}