{"paper":{"title":"$\\mathbb{Q}$-Homology Plane pairs with Logarithmic Kodaira dimension 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sagar Kolte","submitted_at":"2015-12-30T04:06:59Z","abstract_excerpt":"A pair $(S,C)$ is called a singular $\\mathbb{Q}$-homology plane pair if $S$ is a singular projective surface with only quotient singularities having the same rational homology as $\\mathbb{p}^2$ and $C \\subset S$ has the same rational homology as $\\mathbb{p}^1$. We will prove results concerning smooth rational curves on $S$ and the singularities of $S$ such that $\\overline \\kappa(S^0)=1$ and $\\overline \\kappa(S-C) \\neq -\\infty$. We end with an example of such pairs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08840","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"}