Gauss-Manin connections for arrangements, III Formal connections
نویسندگان
چکیده
منابع مشابه
Gauss-manin Connections for Arrangements, Iii Formal Connections
We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a complex rank one local system. We define formal Gauss-Manin connection matrices in the Aomoto complex and prove that, for all arrangements and all local systems, these formal connection matrices specialize to Gauss-Manin connection matrices.
متن کاملGauss-manin Connections for Arrangements
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.
متن کاملGauss-manin Connections for Arrangements, Ii Nonresonant Weights
We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a nonresonant complex rank one local system. Aomoto and Kita determined this GaussManin connection for arrangements in general position. We use their results and an algorithm constructed in this paper to determine this Gauss-Manin connection for all arrangements.
متن کاملGauss-manin Connections for Arrangements, Iv Nonresonant Eigenvalues
An arrangement is a finite set of hyperplanes in a finite dimensional complex affine space. A complex rank one local system on the arrangement complement is determined by a set of complex weights for the hyperplanes. We study the Gauss-Manin connection for the moduli space of arrangements of fixed combinatorial type in the cohomology of the complement with coefficients in the local system deter...
متن کامل0 Gauss - Manin Determinants for Rank 1 Irregular Connections on Curves
Let f : U → Spec (K) be a smooth open curve over a field K ⊃ k, where k is an algebraically closed field of characteristic 0. Let ∇ : L → L ⊗ Ω1U/k be a (possibly irregular) absolutely integrable connection on a line bundle L. A formula is given for the determinant of de Rham cohomology with its Gauß-Manin connection ( detRf∗(L⊗Ω1U/K), det∇GM ) . The formula is expressed as a norm from the curv...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2004
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-04-03621-9