Details:
Title  Gröbner bases via linkage  Author(s)  E. Gorla, J.C. Migliore, U. Nagel  Type  Article in Journal  Abstract  In this paper, we give a sufficient condition for a set G of polynomials to be a Gröbner basis with respect to a given termorder for the ideal I that it generates. Our criterion depends on the linkage pattern of the ideal I and of the ideal generated by the initial terms of the elements of G . We then apply this criterion to ideals generated by minors and pfaffians. More precisely, we consider large families of ideals generated by minors or pfaffians in a matrix or a ladder, where the size of the minors or pfaffians is allowed to vary in different regions of the matrix or the ladder. We use the sufficient condition that we established to prove that the minors or pfaffians form a Gröbner basis for the ideal that they generate, with respect to any diagonal or antidiagonal termorder. We also show that the corresponding initial ideal is Cohen–Macaulay and squarefree, and that the simplicial complex associated to it is vertex decomposable, hence shellable. Our proof relies on known results in liaison theory, combined with a simple Hilbert function computation. In particular, our arguments are completely algebraic.  Keywords  Gröbner bases, Liaison, Determinantal and pfaffian ideals  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S002186931300104X 
Language  English  Journal  Journal of Algebra  Volume  384  Pages  110  134  Year  2013  Edition  0  Translation 
No  Refereed 
No 
