{"paper":{"title":"A boundary divisor in the moduli space of stable quintic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Julie Rana","submitted_at":"2014-07-26T19:26:54Z","abstract_excerpt":"We give a bound on which singularities may appear on Koll\\'ar--Shepherd-Barron--Alexeev stable surfaces for a wide range of topological invariants and use this result to describe all stable numerical quintic surfaces (KSBA-stable surfaces with $K^2=\\chi=5$) whose unique non Du Val singularity is a Wahl singularity. We then extend the deformation theory of Horikawa to the log setting in order to describe the boundary divisor of the moduli space $\\overline{\\mathcal{M}}_{5,5}$ corresponding to these surfaces. Quintic surfaces are the simplest examples of surfaces of general type and the question "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7148","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"}