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I am having some problems to understand the meaning of the following theorem due to Roitmann. I found this theorem in Voisin's book: Hodge Theory and Complex Algebraic Geometry, Volume II, page ...

Let $S$ be a connected smooth complex projective surface. Let $Sym^{d}(S)$, $d\in \mathbb{Z}^+_0$, be the $d$-th symmetric product of $S$ parametrizing $0$-cycles of degree $d$. Let $Sym^{d,d}(S)=...

Let $Sym^m(X)$ be the $m$th symmetric product of a smooth projective variety $X$, $n=\dim(X)$, $Y_1$ an ample hypersurface of $X$, and $CH_0(X)_{hom}$ the Chow groups of $0$-cycles of degree $0$....