Combinatorial construction of toric residues.
Annales de l'Institut Fourier, Volume 55 (2005) no. 2, pp. 511-548.

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 n=2 and for any n 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 n=2 et pour tout n 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.

DOI: 10.5802/aif.2106
Classification: 14M25, 52B20, 06A07
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
Khetan, Amit 1; Soprounov, Ivan 

1 University of Massachusetts, Department of Mathematics and Statistics, Amherst, MA 01003 (USA)
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2106/

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