Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 2, pp. 55-64
Citer cet article
A. G. Khovanskii. An Analog of Determinant Related to Parshin–Kato Theory and Integer Polytopes. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 2, pp. 55-64. http://geodesic.mathdoc.fr/item/FAA_2006_40_2_a5/
@article{FAA_2006_40_2_a5,
author = {A. G. Khovanskii},
title = {An {Analog} of {Determinant} {Related} to {Parshin{\textendash}Kato} {Theory} and {Integer} {Polytopes}},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {55--64},
year = {2006},
volume = {40},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2006_40_2_a5/}
}
TY - JOUR
AU - A. G. Khovanskii
TI - An Analog of Determinant Related to Parshin–Kato Theory and Integer Polytopes
JO - Funkcionalʹnyj analiz i ego priloženiâ
PY - 2006
SP - 55
EP - 64
VL - 40
IS - 2
UR - http://geodesic.mathdoc.fr/item/FAA_2006_40_2_a5/
LA - ru
ID - FAA_2006_40_2_a5
ER -
%0 Journal Article
%A A. G. Khovanskii
%T An Analog of Determinant Related to Parshin–Kato Theory and Integer Polytopes
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2006
%P 55-64
%V 40
%N 2
%U http://geodesic.mathdoc.fr/item/FAA_2006_40_2_a5/
%G ru
%F FAA_2006_40_2_a5
Parshin–Kato theory involves a multilinear function of $n+1$ vectors in the $n$-dimensional vector space over the field $\mathbb{Z}/2\mathbb{Z}$. The same function arises in the computation of the product in the group $(\mathbb{C}^*)^n$ of all roots of several polynomial equations with sufficiently generic Newton polytopes. We discuss this remarkable function and related geometry of integer polytopes.
[1] Khovanskii A., “Newton polyhedrons, a new formula for mixed volume, product of roots of a system of equations”, The Arnoldfest, Proceedings of a conference in honour of V. I. Arnold for his 60th birthday (Toronto, Canada, June 15–21, 1997), Fields Inst. Commun., 24, Amer. Math. Soc., Providence, RI, 1999, 325–364 | MR | Zbl
