The symplectic topology of projective manifolds with small dual

TL;DR

This paper investigates smooth projective varieties with small duals through symplectic topology, revealing their affine parts are subcritical and their hyperplane class is invertible in quantum cohomology, with implications for topology and algebraic geometry.

Contribution

It introduces a symplectic topology approach to small dual varieties, showing their affine parts are subcritical and hyperplane classes are invertible in quantum cohomology, providing new insights.

Findings

Affine parts of small dual varieties are subcritical.

Hyperplane class is invertible in quantum cohomology.

Derived topological and algebraic consequences.

Abstract

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