{"paper":{"title":"Chern slopes of surfaces of general type in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Giancarlo Urz\\'ua, Rodrigo Codorniu","submitted_at":"2015-09-17T13:56:41Z","abstract_excerpt":"Let $\\mathbb{K}$ be an algebraically closed field of characteristic $p>0$, and let $C$ be a nonsingular projective curve over $\\mathbb{K}$. We prove that for any real number $x \\geq 2$, there are minimal surfaces of general type $X$ over $\\mathbb{K}$ such that\n  a) $c_1^2(X)>0, c_2(X)>0$,\n  b) $\\pi_1^{\\text{\\'et}}(X) \\simeq \\pi_1^{\\text{\\'et}}(C)$,\n  c) and $c_1^2(X)/c_2(X)$ is arbitrarily close to $x$.\n  In particular, we show density of Chern slopes in the pathological Bogomolov-Miyaoka-Yau interval $]3,\\infty[$ for any given $p$. Moreover, we prove that for $C=\\mathbb{P}^1$ there exist surf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05260","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":""},"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"}