In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated polytopes are essential. We reduce the problem to finding a collection of partitions of the lattice points in the polytopes satisfying a certain combinatorial property. We use this description to solve the problem when and for any when the polytopes of the divisors share a complete flag of faces. The latter generalizes earlier results when the divisors were all ample.
Dans cet article nous étudions l’existence d’un élément explicite dont le résidu torique est égal à un. On peut trouver un tel élément si et seulement si les polytopes associés sont essentiels. Nous réduisons ce problème à l’existence d’une collection de partitions des points du réseau dans les polytopes qui satisfont une certaine condition combinatoire. Nous utilisons cette description pour résoudre le problème pour et pour tout si les polytopes des diviseurs ont en commun un drapeau complet de faces. Ceci généralise des résultats antérieurs dans le cas où les diviseurs sont amples.
Keywords: Toric varieties, toric residues, semi-ample degrees, facet colorings, combinatorial degree
Mot clés : variétés toriques, résidus toriques, degrés semi-ample, coloriage de facettes, degré combinatoire
@article{AIF_2005__55_2_511_0, author = {Khetan, Amit and Soprounov, Ivan}, title = {Combinatorial construction of toric residues.}, journal = {Annales de l'Institut Fourier}, pages = {511--548}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {2}, year = {2005}, doi = {10.5802/aif.2106}, mrnumber = {2147899}, zbl = {1077.14073}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2106/} }
TY - JOUR AU - Khetan, Amit AU - Soprounov, Ivan TI - Combinatorial construction of toric residues. JO - Annales de l'Institut Fourier PY - 2005 SP - 511 EP - 548 VL - 55 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2106/ DO - 10.5802/aif.2106 LA - en ID - AIF_2005__55_2_511_0 ER -
%0 Journal Article %A Khetan, Amit %A Soprounov, Ivan %T Combinatorial construction of toric residues. %J Annales de l'Institut Fourier %D 2005 %P 511-548 %V 55 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2106/ %R 10.5802/aif.2106 %G en %F AIF_2005__55_2_511_0
Khetan, Amit; Soprounov, Ivan. Combinatorial construction of toric residues.. Annales de l'Institut Fourier, Volume 55 (2005) no. 2, pp. 511-548. doi : 10.5802/aif.2106. http://archive.numdam.org/articles/10.5802/aif.2106/
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