Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator
Annales de l'Institut Fourier, Volume 59 (2009) no. 5, pp. 1715-1752.

Let P(s) be a family of rational polytopes parametrized by inequations. It is known that the volume of P(s) is a locally polynomial function of the parameters. Similarly, the number of integral points in P(s) is a locally quasi-polynomial function of the parameters. Paul-Émile Paradan proved a jump formula for this function, when crossing a wall. In this article, we give an algebraic proof of this formula. Furthermore, we give a residue formula for the jump, which enables us to compute it.

Soit P(s) une famille de polytopes rationnels paramétrés par des inéquations. On sait que le volume de P(s) est une fonction localement polynomiale des paramètres. Similairement, le nombre de points entiers dans P(s) est une fonction localement quasi-polynomiale des paramètres. Paul-Émile Paradan a donné une formule de saut pour cette fonction, lorsqu’on traverse un mur. Dans cet article, nous donnons une démonstration algébrique de ces formules de saut. Nous exprimons aussi le saut, à  l’aide d’une formule de résidus, ce qui permet de le calculer.

Received:
Revised:
Accepted:
DOI: 10.5802/aif.2475
Classification: 52B20,  14M25
Keywords: Polytopes, toric varieties
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Boysal, Arzu; Vergne, Michèle. Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator. Annales de l'Institut Fourier, Volume 59 (2009) no. 5, pp. 1715-1752. doi : 10.5802/aif.2475. https://aif.centre-mersenne.org/articles/10.5802/aif.2475/

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