Vanishing results for the cohomology of complex toric hyperplane complements
AbstractSuppose 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)|.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper 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.
Date of creation: 24 Nov 2011
Date of revision:
hyperplane arrangements; toric arrangements; local systems; L2-cohomology.;
Find related papers by JEL classification:
- L2- - Industrial Organization - - Firm Objectives, Organization, and Behavior - - -
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
If references are entirely missing, you can add them using this form.