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arXiv · 2004.05971

High rank torus actions on contact manifolds

Gianluca Occhetta·Eleonora A. Romano·Luis E. Solá Conde·Jarosław A. Wiśniewski
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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 $\geq \max(2,(n-3)/2)$ 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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Gianluca Occhetta, Eleonora A. Romano, Luis E. Solá Conde, Jarosław A. Wiśniewski. 2020-04-13. High rank torus actions on contact manifolds. https://doi.org/10.1007/s00029-021-00621-w

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