[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://archive.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://archive.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://archive.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://archive.numdam.org/articles/10.5802/aif.1898/
[1] On the Hodge structure of projective hypersurfaces in toric varieties, Duke Math., Volume 75 (1994), pp. 293-338 | MR | Zbl
[2] The homology and shellability of matroids and geometric lattices, Matroid Applications, Cambridge University Press, 1992 | MR | Zbl
[3] Oriented Matroids, Cambridge University Press, 1993 | MR | Zbl
[4] Arrangement of hyperplanes. I. Rational functions and Jeffrey-Kirwan residue, Ann. Sci. École Norm. Sup., Volume 32 (1999), pp. 715-741 | Numdam | MR | Zbl
[5] Residues in toric varieties, Compositio Mathematica, Volume 108 (1997), pp. 35-76 | DOI | MR | Zbl
[6] A global view of residues in the torus, Journal of Pure and Applied Algebra, Volume 117 \& 118 (1997), pp. 119-144 | DOI | MR | Zbl
[7] Residues and resultants, J. Math. Sci. Univ. Tokyo, Volume 5 (1998), pp. 119-148 | MR | Zbl
[8] Rational hypergeometric functions, Compositio Mathematica, Volume 128 (2001), pp. 217-240 | DOI | MR | Zbl
[9] The homogeneous coordinate ring of a toric variety, Journal of Algebraic Geometry, Volume 4 (1995), pp. 17-50 | MR | Zbl
[10] Toric residues, Arkiv för Matematik, Volume 34 (1996), pp. 73-96 | DOI | MR | Zbl
[11] Hypergeometric functions and toral manifolds, Functional Analysis and its Appl., Volume 23 (1989), pp. 94-106 | DOI | MR | Zbl
[12] Generalized Euler integrals and -hypergeometric functions, Advances in Math., Volume 84 (1990), pp. 255-271 | DOI | MR | Zbl
[13] Principles of Algebraic Geometry, John Wiley \& Sons, New York, 1978 | MR | Zbl
[14] The Gauss-Manin connection of the integral of the deformed difference product, Duke Math. J., Volume 92 (1998), pp. 355-379 | MR | Zbl
[15] Syzygies of oriented matroids, Duke Math. J., Volume 111 (2002), pp. 287-317 | DOI | MR | Zbl
[16] Arrangements of Hyperplanes, Grundlehren der mathematisches Wissenchaften, Volume 300, Springer-Verlag, Heidelberg, 1992 | MR | Zbl
[17] Gröbner Bases and Convex Polytopes, American Mathematical Society, Providence, 1995 | MR | Zbl
[18] Gröbner Deformations of Hypergeometric Differential Equations, Algorithms and Computation in Mathematics, Volume 6, Springer-Verlag, Heidelberg, 2000 | MR | Zbl
[19] Multidimensional Residues and Their Applications, American Math. Society, Providence, 1992 | MR | Zbl
[20] Multidimensional hypergeometric functions in conformal field theory, algebraic -theory, algebraic geometry, Proceedings of the International Congress of Mathematicians, (Kyoto, 1990) (Math. Soc. Japan Tokyo), Volume Vol. I, II (1991), pp. 281-300 | Zbl
[21] Facing up to arrangements: face-count formulas for partitions of space by hyperplanes, Memoirs of the AMS, Volume 1 (1975) no. 154 | MR | Zbl
Cité par Sources :
