On piecewise isomorphism of some varieties

Two quasi-projective varieties are called piecewise isomorphic if they can be stratified into pairwise isomorphic strata. We show that the m-th symmetric power $S^m(C^n)$ of the complex affine space $C^n$ is piecewise isomorphic to $C^{mn}$ and the m-th symmetric power $S^m(CP^\infty)$ of the infinite dimensional complex projective space is piecewise isomorphic to the infinite dimensional Grassmannian $Gr(m,\infty)$

Efficient oxide phosphors for light upconversion; green emission from Yb3+ and Ho3+ co-doped Ln(2)BaZnO(5) (Ln = Y, Gd)

This is the author's accepted version of the article. The final published article can be found here: http://dx.doi.org/10.1039/C0JM01652