Geodesic
Birkhoff strata of the~Grassmannian $\mathrm{Gr}^{(2)}$: Algebraic curves
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 448-464

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We study algebraic varieties and curves arising in the Birkhoff strata of the Sato Grassmannian Gr$^{(2)}$. We show that the big cell $\Sigma_0$ contains the tower of families of the normal rational curves of all odd orders. The strata $\Sigma_{2n}$, $n=1,2,3,\dots$, contain hyperelliptic curves of genus $n$ and their coordinate rings. The strata $\Sigma_{2n+1}$, $n=0,1,2,3,\dots$, contain $(2m+1,2m+3)$ plane curves for $n=2m,2m-1$ $(m\geq2)$ and also $(3,4)$ and $(3,5)$ curves in $\Sigma_3$ and $\Sigma_5$. Curves in the strata $\Sigma_{2n+1}$ have zero genus.
Keywords: Sato Grassmannian, Birkhoff stratum, algebraic manifold, hyperelliptic curve. 
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     author = {B. G. Konopelchenko and G. Ortenzi},
     title = {Birkhoff strata of {the~Grassmannian} $\mathrm{Gr}^{(2)}$: {Algebraic} curves},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {448--464},
     publisher = {mathdoc},
     volume = {167},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a9/}
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B. G. Konopelchenko; G. Ortenzi. Birkhoff strata of the~Grassmannian $\mathrm{Gr}^{(2)}$: Algebraic curves. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 448-464. http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a9/