$S^1$-invariant symplectic hypersurfaces in dimension $6$ and the Fano condition

Nicholas Lindsay, Dmitri Panov

We prove that any symplectic Fano $6$-manifold $M$ with a Hamiltonian $S^1$-action is simply connected and satisfies $c_1{c}_2(M)=24$. This is done by showing that the fixed submani…