We prove LeBrun-Salamon conjecture in the following situation: if X is a contact Fano manifold of dimension 2n + 1 whose group of automorphisms is reductive of rank >= max(2, (n - 3)/2) then X is the adjoint variety of a simple group. The rank assumption is fulfilled not only by the three series of classical linear groups but also by almost all the exceptional ones.
High rank torus actions on contact manifolds
Romano, EA;
2021-01-01
Abstract
We prove LeBrun-Salamon conjecture in the following situation: if X is a contact Fano manifold of dimension 2n + 1 whose group of automorphisms is reductive of rank >= max(2, (n - 3)/2) then X is the adjoint variety of a simple group. The rank assumption is fulfilled not only by the three series of classical linear groups but also by almost all the exceptional ones.
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