Birkhoff strata of the Grassmannian Gr(2): Algebraic curves

We study algebraic varieties and curves arising in the Birkhoff strata of the Sato Grassmannian Gr(2). We show that the big cell Σ0 contains the tower of families of the normal rational curves of all odd orders. The strata Σ2n, n = 1, 2, 3,..., contain hyperelliptic curves of genus n and their coordinate rings. The strata Σ2n+1, n = 0, 1, 2, 3,..., contain (2m + 1, 2m + 3) plane curves for n = 2m, 2m - 1 (m ≥ 2) and also (3, 4) and (3, 5) curves in Σ3 and Σ5. Curves in the strata Σ2n+1 have zero genus. © 2011 Pleiades Publishing, Ltd.