HILBERT FUNCTIONS OF MULTIGRADED ALGEBRAS, MIXED MULTIPLICITIES OF IDEALS AND THEIR APPLICATIONS

被引：13

作者：

Trung, N. V. ^{[1
]}

Verma, J. K. ^{[2
]}

机构：

[1] Inst Math, Hanoi 10307, Vietnam

[2] Indian Inst Technol, Dept Math, Bombay 400076, Maharashtra, India

来源：

JOURNAL OF COMMUTATIVE ALGEBRA | 2010年 / 2卷 / 04期

关键词：

Hilbert function; joint reductions; mixed volumes; Rees algebra; fiber cone; associated graded ring; Milnor number; BLOW-UP RINGS; REES-ALGEBRAS; JOINT REDUCTIONS; NUMERICAL CHARACTERIZATION; SEGRE NUMBERS; D-SEQUENCES; DIMENSION; POLYNOMIALS; FORMULA; POWERS;

D O I：

10.1216/JCA-2010-2-4-515

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is a survey on major results on Hilbert functions of multigraded algebras and mixed multiplicities of ideals, including their applications to the computation of Milnor numbers of complex analytic hypersurfaces with isolated singularity, multiplicites of blowup algebras and mixed volumes of polytopes.

引用

页码：515 / 565

页数：51

共 81 条

[1] Intersection numbers, Segre numbers and generalized Samuel multiplicities [J].