Details:
Title  A spherical initial ideal for Pfaffians.  Author(s)  Jakob Jonsson, Volkmar Welker  Type  Article in Journal  Abstract  We determine a term order on the monomials in the variables $\varx{i}{j}$, $1 \leq i < j \leq n$, such that corresponding initial ideal of the ideal of Pfaffians of degree $r$ of a generic $n$ by $n$ skewsymmetric matrix is the StanleyReisner ideal of a join of a simplicial sphere and a simplex. Moreover, we demonstrate that the Pfaffians of the $2r$ by $2r$ skewsymmetric submatrices form a Gr\"obner basis for the given term order. The same methods and similar term orders as for the Pfaffians also yield squarefree initial ideals for certain determinantal ideals. Yet, in contrast to the case of Pfaffians, the corresponding simplicial complexes are balls that do not decompose into a join as above.  ISSN  00192082 
URL 
http://www.math.uiuc.edu/~hildebr/ijm/winter07/final/welker.html 
Language  English  Journal  Ill. J. Math.  Volume  51  Number  4  Pages  13971407  Publisher  University of Illinois, Department of Mathematics, Urbana, IL  Year  2007  Edition  0  Translation 
No  Refereed 
No 
