## arXiv Analytics

### arXiv:2010.07918 [math.AC]AbstractReferencesReviewsResources

#### Convex bodies and graded families of monomial ideals

Published 2020-10-15Version 1

We show that the mixed volumes of arbitrary convex bodies are equal to mixed multiplicities of graded families of monomial ideals, and to normalized limits of mixed multiplicities of monomial ideals. This result evinces the close relation between the theories of mixed volumes from convex geometry and mixed multiplicities from commutative algebra.

Categories: math.AC, math.AG, math.CO
Subjects: 52A39, 13H15, 05E40, 11H06
Related articles: Most relevant | Search more
arXiv:1905.01508 [math.AC] (Published 2019-05-04)
Mixed multiplicities of Divisorial Filtrations
arXiv:0901.0966 [math.AC] (Published 2009-01-08)
On Two Results of Mixed Multiplicities
arXiv:1905.01505 [math.AC] (Published 2019-05-04)
Positivity of Mixed Multiplicities of Filtrations