2017/06/30 by Graham Denham, Graham C. Denham, Alexander I. Suciu
Mathematics · #Abelian group #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic number #Combinatorics #Compactification (mathematics) #Duality (order theory) #Geometric and Algebraic Topology #Hyperplane #Mathematical analysis #Mathematics #Pure mathematics #math.AT #math.CO #math.CV #msc:14M27 #msc:20J05 #msc:32E10 #msc:32S22 #msc:55N25 #msc:55P62 #msc:55R80 #msc:55U30 #msc:57M07
paper · pdf · doi:10.1017/fms.2018.5
published as Forum of Mathematics, Sigma 6 (2018), e6, 20 pages · 14 pages. Some corrections, more details, and updates to references
openalex publication_date 2018/01/01 · arxiv created 2018/03/27 · arxiv updated 2018/06/05 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
We consider smooth, complex quasiprojective varieties U that admit a compactification with a boundary, which is an arrangement of smooth algebraic hypersurfaces. If the hypersurfaces intersect locally like hyperplanes, and the relative interiors of the hypersurfaces are Stein manifolds, we prove that the cohomology of certain local systems on U vanishes. As an application, we show that complements of linear, toric, and elliptic arrangements are both duality and abelian duality spaces.