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 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 $n$ skew-symmetric matrix is the Stanley-Reisner ideal of a join of a simplicial sphere and a simplex. Moreover, we demonstrate that the Pfaffians of the $2r$ by $2r$ skew-symmetric 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 0019-2082 URL http://www.math.uiuc.edu/~hildebr/ijm/winter07/final/welker.html Language English Journal Ill. J. Math. Volume 51 Number 4 Pages 1397--1407 Publisher University of Illinois, Department of Mathematics, Urbana, IL Year 2007 Edition 0 Translation No Refereed No
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