High rank torus actions on contact manifolds

We prove LeBrun–Salamon conjecture in the following situation: if X is a contact Fano manifold of dimension $$2n+1$$ 2 n + 1 whose group of automorphisms is reductive of rank $$\ge \max (2,(n-3)/2)$$ ≥ 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.

Equivariant cohomology of torus orbifolds

We calculate the integral equivariant cohomology, in terms of generators and relations, of locally standard torus orbifolds whose odd degree ordinary cohomology vanishes. We begin by studying GKM-orbifolds, which are more general, before specializing to half-dimensional torus actions.