2011/23  LEM Working Paper Series  
Vanishing results for the cohomology of complex toric hyperplane complements 

Mike W. Davis, Simona Settepanella 

Keywords  
hyperplane arrangements, toric arrangements, local systems,
L2cohomology.


JEL Classifications  


Abstract  
Suppose R is the complement of an essential arrangement of toric
hyperlanes in the complex torus and &pi = π1(R). We show that H*(R;A)
vanishes except in the top degree n when A is one of the following
systems of local coefficients: (a) a system of nonresonant
coefficients in a complex line bundle, (b) the von Neumann algebra N&pi,
or (c) the group ring Zπ. In case (a) the dimension of Hn is the Euler
characteristic, e(R), and in case (b) the nth l2 Betti number is also e(R).


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