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Algebraic varieties and curves arising in Birkhoff strata of the SatoGrassmannian Gr${^{(2)}}$ are studied. It is shown that the big cell $\Sigma_0$contains the tower of families of the normal rational curves of all odd orders.Strata $\Sigma_{2n}$, $n=1,2,3,...$ contain hyperelliptic curves of genus $n$and their coordinate rings. Strata $\Sigma_{2n+1}$, $n=0,1,2,3,...$ contain$(2m+1,2m+3)-$plane curves for $n=2m,2m-1$ $(m \geq 2)$ and $(3,4)$ and $(3,5)$curves in $\Sigma_3$, $\Sigma_5$ respectively. Curves in the strata$\Sigma_{2n+1}$ have zero genus.

Birkhoff strata of the Grassmannian Gr$\mathrm{^{(2)}}$: Algebraic curves