[Résidus binomiaux]
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 -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 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 -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 .
Keywords: binomial residues, hypergeometric functions, Lawrence configurations
Mot clés : résidus binomiaux, fonctions hypergéométriques, configurations de Lawrence
@article{AIF_2002__52_3_687_0,
author = {Cattani, Eduardo and Dickenstein, Alicia and Sturmfels, Bernd},
title = {Binomial residues},
journal = {Annales de l'Institut Fourier},
pages = {687--708},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {52},
number = {3},
year = {2002},
doi = {10.5802/aif.1898},
mrnumber = {1907384},
zbl = {1015.32007},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1898/}
}
TY - JOUR AU - Cattani, Eduardo AU - Dickenstein, Alicia AU - Sturmfels, Bernd TI - Binomial residues JO - Annales de l'Institut Fourier PY - 2002 SP - 687 EP - 708 VL - 52 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1898/ DO - 10.5802/aif.1898 LA - en ID - AIF_2002__52_3_687_0 ER -
%0 Journal Article %A Cattani, Eduardo %A Dickenstein, Alicia %A Sturmfels, Bernd %T Binomial residues %J Annales de l'Institut Fourier %D 2002 %P 687-708 %V 52 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1898/ %R 10.5802/aif.1898 %G en %F AIF_2002__52_3_687_0
Cattani, Eduardo; Dickenstein, Alicia; Sturmfels, Bernd. Binomial residues. Annales de l'Institut Fourier, Tome 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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