2022/06/03 by Siu-Cheong Lau, Lau, Siu-Cheong, Tsung-Ju Lee +3
Physics and Astronomy · #32Q25 #53D37 #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2206.01681
openalex publication_date 2022/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the Landau--Ginzburg superpotential of del Pezzo surfaces can be realized as a limit of their hyperKähler rotation toward the large complex structure limit point. As a corollary, we compute the limit of the complex affine structure of the special Lagrangian fibrations constructed by Collins--Jacob--Lin in P1× P1 arXiv:1904.08363 and compare it with the integral affine structures used in the work of Carl--Pumperla--Siebert arXiv:2205.07753. We also construct the Floer-theoretical Landau--Ginzburg mirrors of smoothing of An-singularities and monotone del Pezzo surfaces, by using the gluing method of Cho--Hong--Lau arXiv:1810.02045 and Hong--Kim--Lau arXiv:1805.11738. They agree with the result of hyperKähler rotation.