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arXiv · 1103.1562

On piecewise isomorphism of some varieties

S. M. Gusein-Zade·I. Luengo·A. Melle-Hernandez
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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 $S^m(CP^\infty)$ of the infinite dimensional complex projective space is piecewise isomorphic to the infinite dimensional Grassmannian $Gr(m,\infty)$.

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S. M. Gusein-Zade, I. Luengo, A. Melle-Hernandez. 2011-03-09. On piecewise isomorphism of some varieties. https://arxiv.org/abs/1103.1562

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