Orbit spaces for torus actions on Hessenberg varieties

In this paper we study effective actions of the compact torus Tn-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 Sn+1 \(U-1 (sic)center dot center dot center dot(sic)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.