Geodesic
Universal and comprehensive Gröbner bases of the classical determinantal ideal
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVII, Tome 373 (2009), pp. 134-143 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $A=(x_{ij}), i=1,2,\dots,k$, $j=1,2,\dots,l$, $1\leq k \leq l$, be a matrix of independent variables, $G$ the set of maximal minors of $A$, $I=(G)$ the classical determinantal ideal. We show that $G$ is a universal Gröbner basis of $I$. Also a sufficient condition of $G$ being a universal comprehensive Gröbner basis is proven. Bibl. – 12 titles. 
@article{ZNSL_2009_373_a8,
     author = {M. Kalinin},
     title = {Universal and comprehensive {Gr\"obner} bases of the classical determinantal ideal},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {134--143},
     year = {2009},
     volume = {373},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a8/}
}
TY  - JOUR
AU  - M. Kalinin
TI  - Universal and comprehensive Gröbner bases of the classical determinantal ideal
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2009
SP  - 134
EP  - 143
VL  - 373
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a8/
LA  - ru
ID  - ZNSL_2009_373_a8
ER  - 
%0 Journal Article
%A M. Kalinin
%T Universal and comprehensive Gröbner bases of the classical determinantal ideal
%J Zapiski Nauchnykh Seminarov POMI
%D 2009
%P 134-143
%V 373
%U http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a8/
%G ru
%F ZNSL_2009_373_a8
M. Kalinin. Universal and comprehensive Gröbner bases of the classical determinantal ideal. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVII, Tome 373 (2009), pp. 134-143. http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a8/

[1] W. Bruns, J. Herzog, Cohen–Macaulay Rings, Cambridge University Press, Cambridge, 1993 | MR | Zbl

[2] W. Bruns, U. Vetter, Determinantal Rings, LNM, 1327, Springer, 1988 | MR | Zbl

[3] B. Sturmfels, “Gröbner bases and Stanley decompositions of determinantal rings”, Mathematische Zeitschrift, 205 (1990), 137–144 | DOI | MR | Zbl

[4] B. Sturmfels, A. Zelevinsky, “Maximal minors and their leading terms”, Adv. Math., 98 (1993), 65–112 | DOI | MR | Zbl

[5] D. Berstein, A. Zelevinsky, “Combinatorics of maximal minors”, J. Algebraic Combinatorics, 2 (1993), 111–121 | DOI | MR

[6] M. Domokos, “Gröbner bases of certain determinantal ideals”, Contrib. Algebra Geometry, 40:2 (1999), 479–493 | MR | Zbl

[7] J. Jonsson, V. Welker, A spherical initial ideal for Pfaffians, arxiv: math/0601335v2 | MR

[8] E. Miller, B. Sturmfels, Combinatorial Commutative Algebra, Graduate Texts in Mathematics, 227, Springer-Verlag, New York, 2004 | MR

[9] V. Weispfenning, “Comprehensive Gröbner bases”, J. Symb. Computat., 14:1 (1992), 1–30 | DOI | MR

[10] V. Weispfenning, “Constructing universal Gröbner bases”, Appl. Algebra, Algebraic Algorithms and Error-Correcting Codes, Proc. AAECC-5, Lecture Notes in Comput. Sci., 356, ed. L. Huguet, 1987, 408–417 | DOI | MR

[11] D. Cox, J. Little, D. O'Shea, Ideals, Varieties and Algorithms, Springer-Verlag, 1991, second corrected edition, 1998

[12] J. Harris, Algebraic Geometry. A First Course, Springer-Verlag, New York, 1992 | MR | Zbl