Convex bodies and graded families of monomial ideals

2020/10/15 by Cid-Ruiz, Yairon, Montaño, Jonathan
#11H06 #13H15 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 52A39 #Secondary 05E40

paper · doi:10.48550/arxiv.2010.07918

Abstract

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.

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