Geodesic
Orbit spaces for torus actions on Hessenberg varieties
Sbornik. Mathematics, Tome 212 (2021) no. 12, pp. 1765-1784

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In this paper we study effective actions of the compact torus $T^{n-1}$ on smooth compact manifolds $M^{2n}$ of even dimension with isolated fixed points. It is proved that under certain conditions on the weight vectors of the tangent representation, the orbit space of such an action is a manifold with corners. In the case of Hamiltonian actions, the orbit space is homotopy equivalent to $S^{n+1} \setminus (U_1 \sqcup \dots \sqcup U_l)$, the complement to the union of disjoint open subsets of the $(n + 1)$-sphere. The results obtained are applied to regular Hessenberg varieties and isospectral manifolds of Hermitian matrices of step type. Bibliography: 23 titles.
Keywords: complexity of the action, Hessenberg varieties.
Mots-clés : torus actions, orbit space 
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     author = {V. V. Cherepanov},
     title = {Orbit spaces for torus actions on {Hessenberg} varieties},
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V. V. Cherepanov. Orbit spaces for torus actions on Hessenberg varieties. Sbornik. Mathematics, Tome 212 (2021) no. 12, pp. 1765-1784. http://geodesic.mathdoc.fr/item/SM_2021_212_12_a5/