2025/01/24 by Konstantin Aleshkin, Aleshkin, Konstantin, Bohan Fang +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Polynomial and algebraic computation #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2501.14222
openalex publication_date 2025/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathcal X=[(\mathbb Cr∖ Z)/G] be a toric Fano orbifold. We compute the Fourier transform of the G-equivariant quantum cohomology central charge of any G-equivariant line bundle on \mathbb Cr with respect to certain choice of parameters. This gives the quantum cohomology central charge of the corresponding line bundle on \mathcal X, while in the oscillatory integral expression it becomes the oscillatory integral in the mirror Landau-Ginzburg mirror of \mathcal X. Moving these parameters to real numbers simultaneously deforms the integration cycle to the mirror Lagrangian cycle of that line bundle. This computation produces a new proof the mirror symmetric Gamma conjecture for \mathcal X.