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Vanishing results for the cohomology of complex toric hyperplane complements
Davis, M. W. (The Ohio State University. Department of Mathematics)
Settepanella, S. (Scuola Superiore Sant’Anna (Pisa, Itàlia))

Data: 2013
Resum: Suppose R is the complement of an essential arrangement of toric hyperlanes in the complex torus (C∗) n and π = 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 π, or (c) the group ring Zπ. In case (a) the dimension of Hn is |e(R)| where e(R) denotes the Euler characteristic, and in case (b) the n th 2 Betti number is also |e(R)|.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Hyperplane arrangements ; Toric arrangements ; Local systems ; L2 -cohomology
Publicat a: Publicacions matemàtiques, Vol. 57, Núm. 2 (2013) , p. 379-392, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_57213_05

14 p, 377.9 KB

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