Abstract
AbstractMotivated by Buchstaber’s and Terzić’s work on the complex Grassmannians \(G_\mathbb {C}(2,4)\) and \(G_\mathbb {C}(2,5)\) we describe the moment map and the orbit space of the oriented Grassmannians \(G_\mathbb {R}^+(2,n)\) under the action of a maximal compact torus. Our main tool is the realisation of these oriented Grassmannians as smooth complex quadric hypersurfaces and the relatively simple Geometric Invariant Theory of the corresponding algebraic torus action.KeywordsOriented GrassmannianComplexity-one T-varietyGIT quotients
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