Abstract:
We consider the problem of the algebraicity of diagonal series for the Laurent expansions of rational functions, geometrically identifiable using the amoeba of the denominator or an integer point in its Newton polyhedron. We give sufficient conditions for the algebraicity of diagonals basing on the theory of multidimensional residues and topological properties of the complements to collections of complex hypersurfaces in complex analytic varieties.
Keywords:diagonal, Laurent series, hyperplane amoeba, separating cycle, local residue, integral representation, algebraic function.