Initial algebras of determinantal rings, Cohen-Macaulay and Ulrich ideals
Winfried Bruns, Tim Römer, and Attila Wiebe
Source: Michigan Math. J. Volume 53, Issue 1
(2005), 71-81.
First Page:
Show
Hide
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.mmj/1114021085
Digital Object Identifier: doi:10.1307/mmj/1114021085
Zentralblatt MATH identifier: 02187045
Mathematical Reviews number (MathSciNet): MR2125534
References
J. P. Brennan, J. Herzog, and B. Ulrich, Maximally generated Cohen--Macaulay modules, Math. Scand. 61 (1987), 181--203.
Mathematical Reviews (MathSciNet): MR947472
W. Bruns and A. Conca, Gröbner bases and determinantal ideals, Commutative algebra, singularities and computer algebra (J. Herzog, V. Vuletescu, eds.), pp. 9--66, Kluwer, Dordrecht, 2003.
Mathematical Reviews (MathSciNet): MR2030262
W. Bruns and J. Gubeladze, Divisorial linear algebra of normal semigroup rings, Algebr. Represent. Theory 6 (2003), 139--168.
Mathematical Reviews (MathSciNet): MR1977927
Digital Object Identifier: doi:10.1023/A:1023295114933
W. Bruns and A. Guerrieri, The Dedekind--Mertens formula and determinantal ideals, Proc. Amer. Math. Soc. 127 (1999), 657--663.
Mathematical Reviews (MathSciNet): MR1468185
Digital Object Identifier: doi:10.1090/S0002-9939-99-04535-9
W. Bruns and J. Herzog, Cohen--Macaulay rings, rev. ed., Cambridge Stud. Adv. Math., 39, Cambridge Univ. Press, Cambridge, 1998.
Mathematical Reviews (MathSciNet): MR1251956
Zentralblatt MATH: 0788.13005
W. Bruns and U. Vetter, Determinantal rings, Lecture Notes in Math., 1327, Springer-Verlag, Berlin, 1988.
Mathematical Reviews (MathSciNet): MR953963
A. Conca, J. Herzog, and G. Valla, Sagbi bases and application to blow-up algebras, J. Reine Angew. Math. 474 (1996), 113--138.
Mathematical Reviews (MathSciNet): MR1390693
P. Doubilet, G.-C. Rota, and J. Stein, On the foundations of combinatorial theory: IX, Combinatorial methods in invariant theory, Stud. Appl. Math. 53 (1974), 185--216.
Mathematical Reviews (MathSciNet): MR498650
S. R. Ghorpade, A note on Hodge's postulation formula for Schubert varieties, Geometric and combinatorial aspects of commutative algebra (J. Herzog, G. Restuccia, eds.), Lecture Notes in Pure and Appl. Math., 217, pp. 211--219, Dekker, New York, 2001.
Mathematical Reviews (MathSciNet): MR1824230
Zentralblatt MATH: 0986.14028
N. Gonciulea and V. Lakshmibai, Degenerations of flag and Schubert varieties to toric varieties, Transform. Groups 1 (1996), 215--248.
Mathematical Reviews (MathSciNet): MR1417711
J. Herzog and N. V. Trung, Gröbner bases and multiplicity of determinantal and Pfaffian ideals, Adv. Math. 96 (1992), 1--37.
Mathematical Reviews (MathSciNet): MR1185786
Digital Object Identifier: doi:10.1016/0001-8708(92)90050-U
M. Hochster, Rings of invariants of tori, Cohen--Macaulay rings generated by monomials, and polytopes, Ann. of Math. (2) 96 (1972), 318--337.
Mathematical Reviews (MathSciNet): MR304376
Digital Object Identifier: doi:10.2307/1970791
JSTOR: links.jstor.org
M. Hochster and J. A. Eagon, Cohen--Macaulay rings, invariant theory, and the generic perfection of determinantal loci, Amer. J. Math. 93 (1971), 1020--1058.
Mathematical Reviews (MathSciNet): MR302643
B. Sturmfels, Algorithms in invariant theory, Springer-Verlag, Vienna, 1993.
Mathematical Reviews (MathSciNet): MR1255980
Zentralblatt MATH: 0802.13002
The Michigan Mathematical Journal