Universal Grobner Bases for Maximal Minors

被引：24

作者：

Conca, Aldo ^{[1
]}

De Negri, Emanuela ^{[1
]}

Gorla, Elisa ^{[2
]}

机构：

[1] Univ Genoa, Dipartimento Matemat, I-16146 Genoa, Italy

[2] Univ Neuchatel, Inst Math, CH-2000 Neuchatel, Switzerland

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2015年 / 2015卷 / 11期

基金：

瑞士国家科学基金会; 美国国家科学基金会;

关键词：

D O I：

10.1093/imrn/rnu032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Bernstein, Sturmfels, and Zelevinsky proved in 1993 that the maximal minors of a matrix of variables form a universal Grobner basis. We present a very short proof of this result, along with broad generalization to matrices with multihomogeneous structures. Our main tool is a rigidity statement for radical Borel fixed ideals in multigraded polynomial rings.

引用

页码：3245 / 3262

页数：18

共 14 条

[1] A Hilbert Scheme in Computer Vision [J].

Aholt, Chris ;

Sturmfels, Bernd ;

Thomas, Rekha .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2013, 65 (05) :961-988

[2]

[Anonymous], 2005, GRAD TEXT M

[3] Bigeneric initial ideals, diagonal subalgebras and bigraded Hilbert functions [J].

Aramova, A ;

Crona, K ;

De Negri, E .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2000, 150 (03) :215-235

[4] COMBINATORICS OF MAXIMAL MINORS [J].

BERNSTEIN, D ;

ZELEVINSKY, A .

JOURNAL OF ALGEBRAIC COMBINATORICS, 1993, 2 (02) :111-121

[5]

Boocher A, 2012, MATH RES LETT, V19, P805

[6] The Hilbert Scheme of the Diagonal in a Product of Projective Spaces [J].

Cartwright, Dustin ;

Sturmfels, Bernd .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2010, 2010 (09) :1741-1771

[7]

CoCoA Team, COCOA SYST DOING COM

[8] Linear spaces, transversal polymatroids and ASL domains [J].

Conca, Aldo .

JOURNAL OF ALGEBRAIC COMBINATORICS, 2007, 25 (01) :25-41

[9]

Eisenbud D., 1995, Commutative Algebra with a View Toward Algebraic Geometry

[10]

Herzog J, 2011, GRAD TEXTS MATH, V260, P3, DOI 10.1007/978-0-85729-106-6

← 1 2 →