Geodesic
LOCAL SYSTEMS ON COMPLEMENTS OF ARRANGEMENTS OF SMOOTH, COMPLEX ALGEBRAIC HYPERSURFACES
Forum of Mathematics, Sigma, Tome 6 (2018)

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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. 
@article{10_1017_fms_2018_5,
     author = {GRAHAM DENHAM and ALEXANDER I. SUCIU},
     title = {LOCAL {SYSTEMS} {ON} {COMPLEMENTS} {OF} {ARRANGEMENTS} {OF} {SMOOTH,} {COMPLEX} {ALGEBRAIC} {HYPERSURFACES}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {6},
     year = {2018},
     doi = {10.1017/fms.2018.5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2018.5/}
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GRAHAM DENHAM; ALEXANDER I. SUCIU. LOCAL SYSTEMS ON COMPLEMENTS OF ARRANGEMENTS OF SMOOTH, COMPLEX ALGEBRAIC HYPERSURFACES. Forum of Mathematics, Sigma, Tome 6 (2018). doi: 10.1017/fms.2018.5

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