Convex bodies and graded families of monomial ideals

• Yairon Cid-Ruiz ^[1] ; Jonathan Montaño ^[2]
  1. [1] Ghent University

     Ghent University

     Arrondissement Gent, Bélgica

     
  2. [2] New Mexico State University

     New Mexico State University

     Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 6, 2022, págs. 2033-2056
• Idioma: inglés
• DOI: 10.4171/RMI/1373
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• Resumen

  • 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