Displaying similar documents to “Gauss-Manin connections of Schläfli type for hypersphere arrangements”

Binomial residues

Eduardo Cattani, Alicia Dickenstein, Bernd Sturmfels (2002)

Annales de l’institut Fourier

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A binomial residue is a rational function defined by a hypergeometric integral whose kernel is singular along binomial divisors. Binomial residues provide an integral representation for rational solutions of A -hypergeometric systems of Lawrence type. The space of binomial residues of a given degree, modulo those which are polynomial in some variable, has dimension equal to the Euler characteristic of the matroid associated with A .

On some algebraic identities and the exterior product of double forms

Mohammed Larbi Labbi (2013)

Archivum Mathematicum

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We use the exterior product of double forms to free from coordinates celebrated classical results of linear algebra about matrices and bilinear forms namely Cayley-Hamilton theorem, Laplace expansion of the determinant, Newton identities and Jacobi’s formula for the determinant. This coordinate free formalism is then used to easily generalize the previous results to higher multilinear forms namely to double forms. In particular, we show that the Cayley-Hamilton theorem once applied to...

Nonresonance conditions for arrangements

Daniel C. Cohen, Alexandru Dimca, Peter Orlik (2003)

Annales de l’institut Fourier

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We prove a vanishing theorem for the cohomology of the complement of a complex hyperplane arrangement with coefficients in a complex local system. This result is compared with other vanishing theorems, and used to study Milnor fibers of line arrangements, and hypersurface arrangements.