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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 167, Number 3, Pages 448–464
DOI: https://doi.org/10.4213/tmf6653
(Mi tmf6653)
 

This article is cited in 3 scientific papers (total in 3 papers)

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

B. G. Konopelchenkoab, G. Ortenzic

a INFN, Sezione di Lecce, Lecce, Italy
b Dipartimento di Fisica, Università del Salento, Sezione di Lecce, Lecce, Italy
c Dipartimento di Matematica Pura ed Applicazioni, Università di Milano Bicocca, Milano, Italy
Full-text PDF (469 kB) Citations (3)
References:
Abstract: 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.
Received: 23.06.2011
English version:
Theoretical and Mathematical Physics, 2011, Volume 167, Issue 3, Pages 785–799
DOI: https://doi.org/10.1007/s11232-011-0062-6
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: B. G. Konopelchenko, G. Ortenzi, “Birkhoff strata of the Grassmannian $\mathrm{Gr}^{(2)}$: Algebraic curves”, TMF, 167:3 (2011), 448–464; Theoret. and Math. Phys., 167:3 (2011), 785–799
Citation in format AMSBIB
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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