A Gorenstein simplicial complex for symmetric minors
  We show that the ideal generated by the $(n-2)$ minors of a general symmetric $n$ by $n$ matrix has an initial ideal that is the Stanley-Reisner ideal of the boundary complex of a simplicial polytope and has the same Betti numbers. 
Aldo Conca, Emanuela de Negri, Volkmar Welker
math.AC