Lagrangian Floer potential of orbifold spheres

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• 作者：Cheol-Hyun Cho^a ; ^{chocheol@snu.ac.kr} ; Hansol Hong^a ; ^{hansol84@gmail.com} ; Sang-hyun Kim^a ; ^{s.kim@snu.ac.kr} ; Siu-Cheong Lau^b ; ^{s.lau@math.harvard.edu}
• 关键词：Lagrangian Floer homology ; Potential ; Mirror symmetry ; Holomorphic discs ; Mirror map ; Orbifold
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：14 January 2017
• 年：2017
• 卷：306
• 期：Complete
• 页码：344-426
• 全文大小：3226 K
• 卷排序：306

文摘

For each sphere with three orbifold points, we construct an algorithm to compute the open Gromov–Witten potential, which serves as the quantum-corrected Landau–Ginzburg mirror and is an infinite series in general. This gives the first class of general-type geometries whose full potentials can be computed. As a consequence we obtain an enumerative meaning of mirror maps for elliptic curve quotients. Furthermore, we prove that the open Gromov–Witten potential is convergent, even in the general-type cases, and has an isolated singularity at the origin, which is an important ingredient of proving homological mirror symmetry.