{"paper":{"title":"Burniat surfaces III: deformations of automorphisms and extended Burniat surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fabrizio Catanese (Universitaet Bayreuth), Ingrid Bauer","submitted_at":"2010-12-16T22:12:55Z","abstract_excerpt":"We continue our investigation of the connected components of the moduli space of surfaces of general type containing the Burniat surfaces, correcting a mistake in part II. We define the family of extended Burniat surfaces with K_S^2 = 4, resp. 3, and prove that they are a deformation of the family of nodal Burniat surfaces with K_S^2 = 4, resp. 3. We show that the extended Burniat surfaces together with the nodal Burniat surfaces with K_S^2=4 form a connected component of the moduli space. We prove that the extended Burniat surfaces together with the nodal Burniat surfaces with K_S^2=3 form an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3770","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"}