{"paper":{"title":"Inequalities of Chern classes on nonsingular projective $n$-folds of Fano and general type with ample canonical bundle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hao Sun, Rong Du","submitted_at":"2017-12-10T00:35:22Z","abstract_excerpt":"Let $X$ be a nonsingular projective $n$-fold $(n\\ge 2)$ of Fano or of general type with ample canonical bundle $K_X$ over an algebraic closed field $\\kappa$ of any characteristic. We produce a new method to give a bunch of inequalities in terms of all the Chern classes $c_1, c_2, \\cdots, c_n$ by pulling back Schubert classes in the Chow group of Grassmannian under the Gauss map. Moreover, we show that if the characteristic of $\\kappa$ is $0$, then the Chern ratios $(\\frac{c_{2,1^{n-2}}}{c_{1^n}}, \\frac{c_{2,2,1^{n-4}}}{c_{1^n}}, \\cdots, \\frac{c_{n}}{c_{1^n}})$ are contained in a convex polyhed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03458","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":""},"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"}