The pole assignment problems of linear system by decentralized static output feedback are considered in this paper. A compactification of decentralized static feedback space, product Grassmannians, is introduced in this paper. Its degree under Plucker-Segre embedding is computed. Sufficient conditions for arbitrary and almost arbitrary pole assignability are given. It is also proved that the generic m x p system of McMillan degree n has arbitrary pole assignability by r-channel decentralized static output with mi inputs and pi outputs on the ith channel if SIGMA(i=1)r m(i)p(i) greater-than-or-equal-to n when the degree of the product Grassmannians is odd, or if SIGMA(i=1)r m(i)p(i) > n and the local channels have either the same numbers of inputs or the same numbers of outputs when the degree of the product Grassmannians is even.