Resonant local systems on complements of discriminantal arrangements and s-fraktur sign l-fraktur sign2 representations
Document Type
Article
Publication Date
1-1-2003
Abstract
We calculate the skew-symmetric cohomology of the complement of a discriminantal hyperplane arrangement with coefficients in local systems arising in the context of the representation theory of the Lie algebra s-fraktur sign l-fraktur sign2. For a discriminantal arrangement in Ck, the skew-symmetric cohomology is nontrivial in dimension k - 1 precisely when the 'master function' which defines the local system on the complement has nonisolated critical points. In symmetric coordinates, the critical set is a union of lines. Generically, the dimension of this nontrivial skew-symmetric cohomology group is equal to the number of critical lines.
Publication Source (Journal or Book title)
Geometriae Dedicata
First Page
217
Last Page
234
Recommended Citation
Cohen, D., & Varchenko, A. (2003). Resonant local systems on complements of discriminantal arrangements and s-fraktur sign l-fraktur sign2 representations. Geometriae Dedicata, 101 (1), 217-234. https://doi.org/10.1023/A:1026370732724