Differentially fixed ideals in affine semigroup rings

被引：0
|
作者：
Miller, Lance Edward [1 ]
Taylor, William D. [2 ]
Vassilev, Janet [3 ]
机构：
[1] Univ Arkansas, Dept Math Sci, 355 SCEN, Fayetteville, AR 72701 USA
[2] Tennessee State Univ, Dept Math Sci, Boswell Hall 316B, Nashville, TN 37209 USA
[3] Univ New Mexico, Dept Math & Stat, MSC01 1115, Albuquerque, NM 87131 USA
来源：
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2023年
关键词：
Toric rings; differential operators; polyhedral face data; MULTIPLIER IDEALS; OPERATORS; MODULES;
D O I：
10.1142/S0218196723500509
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a complete characterization of when monomial ideals are fixed by differential operators of affine semigroup rings over DOUBLE-STRUCK CAPITAL C. Perhaps surprisingly, every monomial ideal is fixed by an infinite set of homogeneous differential operators and is in fact determined by them. This opens up a new tool for studying monomial ideals. We explore applications of this to (mixed) multiplier ideals and other variants as well as give examples of detecting ideal membership in integrally closed powers and symbolic powers of squarefree monomial ideals.
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页码：1127 / 1156
页数：30
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