Abelian Coverings of the Complex Projective Plane Branched along Configurations of Real Lines.

Intro -- Contents -- Introduction -- I. Preliminaries -- I.1 Branched coverings of smooth varieties -- I.2 The topology of branched coverings -- I.3 Inertia and stabilizer subgroups -- I.4 Criterion for smoothness of coverings -- I.5 First Betti number and Picard number -- II. Intersections of Curves on Covering Surfaces -- II.1 Lifting data -- II.2 Intersection graphs -- II.3 Intersection formulas for covering surfaces -- III. Hirzebruch Covering Surfaces -- III.1 Hirzebruch covering surfaces -- III.2 Fibrations and monodromy -- III.3 Fundamental group of the complement of real lines -- III.4 Lifting data for the branch locus -- IV. Algorithm for Computing the First Betti Number -- IV.1 Input -- IV.2 Step 1: First Betti number of unbranched part -- IV.3 Step 2: Intersection matrix for curves above branch locus -- V. Examples -- V.1 Classification of Hirzebruch coverings -- V.2 Lines in general position -- V.3 Fibrations -- V.4 Coverings birational to the product of two curves -- V.5 K3 surfaces and elliptic surfaces -- V.6 Calculations of invariants -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.