Decompositions of ideals of minors meeting a submatrix
  We compute the primary decomposition of certain ideals generated by subsets of minors in a generic matrix or in a generic symmetric matrix, or subsets of Pfaffians in a generic skew-symmetric matrix. Specifically, the ideals we consider are generated by minors that have at least some given number of rows and columns in certain submatrices. 
Kent M. Neuerburg and Zach Teitler
math.AC