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.

Konopelchenko, B., Ortenzi, G. (2011). Birkhoff strata of the Grassmannian Gr(2): Algebraic curves. THEORETICAL AND MATHEMATICAL PHYSICS, 167(3), 785-799 [10.1007/s11232-011-0062-6].

### 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 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.
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Articolo in rivista - Articolo scientifico
algebraic manifold; Birkhoff stratum; hyperelliptic curve; Sato Grassmannian; Mathematical Physics; Statistical and Nonlinear Physics
English
2011
167
3
785
799
none
Konopelchenko, B., Ortenzi, G. (2011). Birkhoff strata of the Grassmannian Gr(2): Algebraic curves. THEORETICAL AND MATHEMATICAL PHYSICS, 167(3), 785-799 [10.1007/s11232-011-0062-6].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/56806
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