Gauss-Manin Connections for Arrangements

Details Gauss-Manin Connections for Arrangements Gauss-Manin Connections for Arrangements

2001-05-09

arxiv.org/abs/math/0105063v3

Compositio Math. 136 (2003), 299-316

Mathematics

Algebraic Geometry

LaTeX, 15 pages. v2: minor changes. v3: 16 pages, to appear in Compositio Math

Scientific paper

We construct a formal connection on the Aomoto complex of an arrangement of
hyperplanes, and use it to study the Gauss-Manin connection for the moduli
space of the arrangement in the cohomology of a complex rank one local system.
We prove that the eigenvalues of the Gauss-Manin connection are integral linear
combinations of the weights which define the local system.

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