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We study smooth projective varieties with small dual variety using methodsfrom symplectic topology. We prove the affine parts of such varieties aresubcritical, and that the hyperplane class is invertible in their quantumcohomology. We derive several topological and algebraic geometric consequencesfrom that. The main tool in our work is the Seidel representation associated toHamiltonian fibrations.

The symplectic topology of projective manifolds with small dual