{"paper":{"title":"A sharp slope inequality for general stable fibrations of curves","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Atsushi Moriwaki","submitted_at":"1996-01-05T15:38:29Z","abstract_excerpt":"Let M_g be the moduli space of stable curves of genus g >= 2. Let D_i be the irreducible component of the boundary of M_g such that general points of D_i correspond to stable curves with one node of type i. Let M_g^0 be the set of stable curves that have at most one node of type i>0. Let d_i be the class of D_i in Pic(M_g)_Q and h the Hodge class on M_g. In this paper, we will prove a sharp slope inequality for general stable fibrations. Namely, if $C$ is a complete curve on M_g^0, then ( (8g+4)h - g d_0 - \\sum_{i=1}^{[g/2]} 4i(g-i) d_i . C ) >= 0. As an application, we can prove effective Bog"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9601003","kind":"arxiv","version":1},"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"}