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

Abstract

We study algebraic varieties and curves arising in the Birkhoff strata of the Sato Grassmannian Gr (2) . We show that the big cell Σ 0 contains the tower of families of the normal rational curves of all odd orders. The strata Σ 2n, n = 1, 2, 3,..., contain hyperelliptic curves of genus n and their coordinate rings. The strata Σ 2n+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 Σ 3 and Σ 5 . Curves in the strata Σ 2n+1 have zero genus.