2025/05/08 by Jishnu Bose, Bose, Jishnu, Harold Williams +1
Mathematics · Physics and Astronomy · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2505.05012
The coherent-constructible correspondence is a realization of toric mirror symmetry in which the A-side is modeled by constructible sheaves on Tn. This paper provides a geometric realization of the mirror Picard group action in this correspondence, characterizing it in terms of quantized contact isotopies and providing a sheaf-theoretic counterpart to work of Hanlon in the Fukaya-Seidel setting. Given a toric Cartier divisor D, we consider a family of homogeneous Hamiltonians Hε on T^* Tn. Their flows act on sheaves via a family of kernels Kε on Tn × Tn. The nearby cycles kernel K0 corresponds heuristically to the Hamiltonian flow of the non-differentiable function limε → 0 Hε, which is the pullback of the support function of D along the cofiber projection. We show that the action of K0 coincides with the convolution action of the associated twisted polytope sheaf, hence mirrors the action of O(D) on coherent sheaves.