Convex bodies and graded families of monomial ideals

被引：0
作者：
Cid-Ruiz, Yairon [1 ]
Montano, Jonathan [2 ]
机构：
[1] Univ Ghent, Dept Math Algebra & Geometry, Krijgslaan 281,Bldg S25, B-9000 Ghent, Belgium
[2] New Mexico State Univ, Dept Math Sci, POB 30001, Las Cruces, NM 88003 USA
来源：
REVISTA MATEMATICA IBEROAMERICANA | 2022年 / 38卷 / 06期
基金：
美国国家科学基金会;
关键词：
Convex bodies; graded families; mixed volume; mixed multiplicity; MIXED MULTIPLICITIES; ALGEBRAS; NUMBERS;
D O I：
10.4171/RMI/1373
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：2033 / 2056
页数：24
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