{"paper":{"title":"Moduli spaces and braid monodromy types of bidouble covers of the quadric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AG","authors_text":"Bronislaw Wajnryb (Technical University of Rzeszow), Fabrizio Catanese (Universitaet Bayreuth), Michael L\\\"onne (Universitaet Goettingen)","submitted_at":"2009-10-12T17:31:40Z","abstract_excerpt":"Bidouble covers $\\pi : S \\mapsto Q$ of the quadric Q are parametrized by connected families depending on four positive integers a,b,c,d. In the special case where b=d we call them abc-surfaces.\n  Such a Galois covering $\\pi$ admits a small perturbation yielding a general 4-tuple covering of Q with branch curve $\\De$, and a natural Lefschetz fibration obtained from a small perturbation of the composition of $ \\pi$ with the first projection.\n  We prove a more general result implying that the braid monodromy factorization corresponding to $\\De$ determines the three integers a,b,c in the case of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2142","kind":"arxiv","version":2},"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"}