Resumen de Convex bodies and graded families of monomial ideals

Yairon Cid Ruiz, Jonathan Montaño

• 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