{"paper":{"title":"The numerical equivalence relation for height functions and ampleness and nefness criteria for divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Chong Gyu Lee","submitted_at":"2010-10-19T15:32:08Z","abstract_excerpt":"In this paper, we study properties of Weil height functions associated with numerically trivial divisors.\n  It helps us to define the fractional limit of $h_E$ with respect to $h_D$ on $U$, with $D$ ample:\n  \\[\n  \\Flim_D(E,U) := \\liminf_{\\substack{P \\in U h_D(P) \\rightarrow \\infty}}\\dfrac{h_E(P)}{h_D(P)}.\n  \\]\n  The value of $\\Flim_D(E,U)$ contains numerical information about a divisor $E$, enough to determine whether $E$ is ample, numerically effective or pseudo-effective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3954","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"}