On piecewise isomorphism of some varieties

Abstract

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 $S^m(C{P}^{\infty })$ of the infinite dimensional complex projective space is piecewise isomorphic to the infinite dimensional Grassmannian $Gr(m,\infty )$.

Cited by in corpus (1)

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