{"paper":{"title":"On the multiplicity of reducible relative stable morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Nobuyoshi Takahashi","submitted_at":"2017-11-22T08:28:44Z","abstract_excerpt":"Let $(Z, D)$ be a pair of a smooth surface and a smooth anti-canonical divisor. Denote by $\\mathfrak{M}_\\beta$ the moduli stack of genus $0$ relative stable morphisms of class $\\beta$ with full tangency to the boundary. Let $C_1$ and $C_2$ be rational curves fully tangent to $D$ at the same point $P$ and assume that $C_1$ and $C_2$ are immersed and that $(C_1.C_2)_P=\\min\\{D.C_1, D.C_2\\}$. Then we show that the contribution of $C_1\\cup C_2$ to the virtual count of $\\mathfrak{M}_{[C_1]+[C_2]}$ is $\\min\\{D.C_1, D.C_2\\}$.\n  As an example, we describe genus $0$ relative stable morphisms to $(\\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08173","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"}