Local systems on complements of arrangements of smooth, complex algebraic hypersurfaces

Abstract

We consider smooth, complex quasi-projective varieties $U$ which 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.

14 pages. Some corrections, more details, and updates to references

References in corpus (9)

• Formality properties of finitely generated groups and Lie algebras
• Combinatorial covers and vanishing of cohomology
• Abelian duality and propagation of resonance
• Topology of subvarieties of complex semi-abelian varieties
• Computing cohomology of configuration spaces
• Mellin transformation, propagation, and abelian duality spaces
• Complements of hyperplane arrangements as posets of spaces
• The l^2-cohomology of hyperplane complements
• Cohomology of the complement to an elliptic arrangement

Cited by in corpus (8)

• Cohomology rings of compactifications of toric arrangements
• Perverse sheaves on semi-abelian varieties
• Formality and finiteness in rational homotopy theory
• Homology of tropical fans
• Mellin transformation, propagation, and abelian duality spaces
• Milnor fibrations of arrangements with trivial algebraic monodromy
• Algebraic invariants of orbit configuration spaces in genus zero associated to finite groups
• Orbit configuration space of standard action and cellular methods of poset