Resonant local systems on complements of discriminantal arrangements and sl_2 representations

Details Resonant local systems on complements of discriminantal arrangements and sl_2 representations Resonant local systems on complements of discriminantal arrangements and sl_2 representations

2002-11-16

arxiv.org/abs/math/0211253v1

Geom. Dedicata 101 (2003), 217-234

Mathematics

Algebraic Geometry

LaTeX, 12 pages

Scientific paper

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 sl_2. For a discriminantal arrangement in C^k, 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.

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