Binomial residues
Annales de l'Institut Fourier, Volume 52 (2002) no. 3, pp. 687-708.

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.

Un résidu binomial est une fonction rationnelle définie par une intégrale hypergéométrique ayant un noyau singulier le long d’un diviseur binomial. Les résidus binomiaux donnent une représentation intégrale des solutions rationnelles des systèmes A-hypergéométriques du type de Lawrence. L’espace des résidus binomiaux d’un degré donné, modulo ceux qui dépendent polynomialement d’une des variables, a sa dimension égale à la caractéristique d’Euler du matroïde associé à A.

DOI: 10.5802/aif.1898
Classification: 05B35,  14M25,  32A27
Keywords: binomial residues, hypergeometric functions, Lawrence configurations
Cattani, Eduardo 1; Dickenstein, Alicia 2; Sturmfels, Bernd 3

1 University of Massachusetts, Department of Mathematics and Statistics, Amherst MA 01003 (USA)
2 Universidad de Buenos Aires, Departamento de Matematica, FCEyN (1428), Buenos Aires (Argentine)
3 University of California, Department of Mathematics, Berkeley CA 94720(USA)
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Cattani, Eduardo; Dickenstein, Alicia; Sturmfels, Bernd. Binomial residues. Annales de l'Institut Fourier, Volume 52 (2002) no. 3, pp. 687-708. doi : 10.5802/aif.1898. http://www.numdam.org/articles/10.5802/aif.1898/

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