Decomposition of perverse sheaves on plane line arrangements

Abstract

ABSTRACTOn the complement to a central plane line arrangement , a locally constant sheaf of complex vector spaces ℒa is associated to any multi-index a∈ℂn. Using the description of MacPherson and Vilonen of the category of perverse sheaves [7, 8], we obtain a criterion for the irreducibility and number of decomposition factors of the direct image as a perverse sheaf, where j:X→ℂ2 is the canonical inclusion.