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

Abstract

Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian 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 $n=2m,2m-1$ $(m\ge 2)$ and $(3,4)$ and $(3,5)$ curves in ${\Sigma }_3$, ${\Sigma }_5$ respectively. Curves in the strata ${\Sigma }_{2n+1}$ have zero genus.

14 pages, no figures, improved some definitions, typos corrected

References in corpus (2)

• Singular sector of the Burgers-Hopf hierarchy and deformations of hyperelliptic curves
• Algebraic varieties in Birkhoff strata of the Grassmannian Gr${}^{(2)}$: Harrison cohomology and integrable systems

Cited by in corpus (2)

• Algebraic varieties in Birkhoff strata of the Grassmannian Gr${}^{(2)}$: Harrison cohomology and integrable systems
• Cohomological, Poisson structures and integrable hierarchies in tautological subbundles for Birkhoff strata of Sato Grassmannian