2024/03/23 by Špela Špenko, Michel Van den Bergh, Špenko, Špela +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Boundary (topology) #FOS: Mathematics #Geometry #Homogeneous space #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2403.15660
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a projective crepant resolution of a Gorenstein affine toric variety and let ((ℂ^*)k,f) be the LG-model which is the Hori-Vafa mirror dual of X. Let D be a generic fiber of f equipped with the restriction of the standard Liouville form on (ℂ^*)k. Let KA be the so-called "stringy Kähler moduli space" of X. We show that π1(KA) acts on the wrapped Fukaya category of D. Using results by Gammage - Shende and Zhou, this result implies that π1(KA) acts on Db(coh(∂ X)) where ∂ X is the toric boundary divisor of X. We show that the induced action of π1(KA) on K0(coh(∂ X)) may be extended in a natural way to an action on K0(X) which corresponds to a GKZ system.