Sheaves on \(\mathbb{P}^{1}\times \mathbb{P}^{1}\), bigraded resolutions, and coadjoint orbits of loop groups (Q2855893)
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scientific article; zbMATH DE number 6218144
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sheaves on \(\mathbb{P}^{1}\times \mathbb{P}^{1}\), bigraded resolutions, and coadjoint orbits of loop groups |
scientific article; zbMATH DE number 6218144 |
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23 October 2013
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Sheaves
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integrable systems
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Sheaves on \(\mathbb{P}^{1}\times \mathbb{P}^{1}\), bigraded resolutions, and coadjoint orbits of loop groups (English)
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The aim of this paper is to present a variation on a theme developed by several authors, notably Moser, Adams, Harnad, Hurtubise, Previato and relating integrable systems, rank \(r\) perturbations, spectral curves and their Jacobians, and coadjoint orbits of loop groups. The authors construct a canonical linear resolution of acyclic \(1\)-dimensional sheaves on \(\mathbb{P}^1\times \mathbb{P}^1\) and discuss the resulting natural Poisson structure.
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