We begin developing a theory of morphisms of moduli spaces of pseudoholomorphic curves and discs with Lagrangian boundary conditions as Kuranishi spaces, using a modification of the procedure of Fukaya-Oh-Ohta-Ono. As an example, we consider the total space of the line bundles O(−n) and O on P1 as toric Kähler manifolds, and we construct isomorphic Kuranishi structures on the moduli space of holomorphic discs in O(−n) on P1 with boundary on a moment map fiber Lagrangian L and on a moduli space of holomorphic discs subject to appropriate tangency conditions in O. We then deform this latter Kuranishi space and use this deformation to define a Lagrangian potential for L in O(−n), and hence a superpotential for O(−n). With some conjectural assumptions regarding scattering diagrams in P1 × P, this superpotential can then be calculated tropically analogously to a bulk-deformed potential of a Lagrangian in P1 × P1.
| Identifer | oai:union.ndltd.org:bu.edu/oai:open.bu.edu:2144/48497 |
| Date | 26 March 2024 |
| Creators | Bardwell-Evans, Sam A. |
| Contributors | Lin, Yu-Shen |
| Source Sets | Boston University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
| Rights | Attribution-NonCommercial 4.0 International, http://creativecommons.org/licenses/by-nc/4.0/ |
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