JournalsrmiVol. 38, No. 6pp. 2033–2056

Convex bodies and graded families of monomial ideals

  • Yairon Cid-Ruiz

    Ghent University, Belgium

  • Jonathan Montaño

    New Mexico State University, Las Cruces, USA
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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.

Cite this article

Yairon Cid-Ruiz, Jonathan Montaño, Convex bodies and graded families of monomial ideals. Rev. Mat. Iberoam. 38 (2022), no. 6, pp. 2033–2056

DOI 10.4171/RMI/1373