{"paper":{"title":"The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Masataka Iwai, Satoshi Jinnouchi, Shiyu Zhang","submitted_at":"2025-07-11T12:17:16Z","abstract_excerpt":"We establish the Miyaoka-Yau inequality for $n$-dimensional projective klt varieties with big canonical divisor $K_X$: \\[ (2(n+1)\\widehat{c}_2(X) - n \\widehat{c}_1(X)^2) \\cdot \\langle c_1(K_X)^{n-2} \\rangle \\ge 0. \\] We also prove the Miyaoka-Yau inequality for K-semistable projective klt varieties with big anticanonical divisor $-K_X$. As part of our approach, we define the non-pluripolar product $\\langle \\alpha_1 \\cdots \\alpha_p \\rangle$ on singular varieties, and establish the Bogomolov-Gieseker type inequality for $\\langle \\alpha^{n-1} \\rangle$-semistable Higgs sheaves with respect to a bi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.08522","kind":"arxiv","version":2},"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/2507.08522/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"}