Geodesic
Convex bodies and multiplicities of ideals
Informatics and Automation, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 291-307

Voir la notice de l'article provenant de la source Math-Net.Ru

We associate convex regions in $\mathbb R^n$ to $\mathfrak m$-primary graded sequences of subspaces, in particular $\mathfrak m$-primary graded sequences of ideals, in a large class of local algebras (including analytically irreducible local domains). These convex regions encode information about Samuel multiplicities. This is in the spirit of the theory of Gröbner bases and Newton polyhedra on the one hand, and the theory of Newton–Okounkov bodies for linear systems on the other hand. We use this to give a new proof as well as a generalization of a Brunn–Minkowski inequality for multiplicities due to Teissier and Rees–Sharp. 
@article{TRSPY_2014_286_a15,
     author = {Kiumars Kaveh and Askold Khovanskii},
     title = {Convex bodies and multiplicities of ideals},
     journal = {Informatics and Automation},
     pages = {291--307},
     publisher = {mathdoc},
     volume = {286},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_286_a15/}
}
TY  - JOUR
AU  - Kiumars Kaveh
AU  - Askold Khovanskii
TI  - Convex bodies and multiplicities of ideals
JO  - Informatics and Automation
PY  - 2014
SP  - 291
EP  - 307
VL  - 286
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2014_286_a15/
LA  - en
ID  - TRSPY_2014_286_a15
ER  - 
%0 Journal Article
%A Kiumars Kaveh
%A Askold Khovanskii
%T Convex bodies and multiplicities of ideals
%J Informatics and Automation
%D 2014
%P 291-307
%V 286
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2014_286_a15/
%G en
%F TRSPY_2014_286_a15
Kiumars Kaveh; Askold Khovanskii. Convex bodies and multiplicities of ideals. Informatics and Automation, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 291-307. http://geodesic.mathdoc.fr/item/TRSPY_2014_286_a15/