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Vanishing results for the cohomology of complex toric hyperplane complements

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  • Mike W. Davis
  • Simona Settepanella
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    Abstract

    Suppose R is the complement of an essential arrangement of toric hyperlanes in the complex torus and ? = ?1(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?, or (c) the group ring Z?. 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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    Bibliographic Info

    Paper provided by Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy in its series LEM Papers Series with number 2011/23.

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    Date of creation: 24 Nov 2011
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    Handle: RePEc:ssa:lemwps:2011/23

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    Keywords: hyperplane arrangements; toric arrangements; local systems; L2-cohomology.;

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