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We study smooth projective varieties with small dual variety using methods from symplectic topology. For such varieties, we prove that the hyperplane class is an invertible element in the quantum cohomology of their hyperplane sections. We also prove that the affine part of such varieties are subcritical. We derive several topological and algebraic geometric consequences from that. The main tool in our work is the Seidel representation associated to Hamiltonian fibrations.

The Symplectic Topology of Projective Manifolds with Small Dual