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Morphisms and regularization of moduli spaces of pseudoholomorphic discs with Lagrangian boundary conditions

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.

Identiferoai:union.ndltd.org:bu.edu/oai:open.bu.edu:2144/48497
Date26 March 2024
CreatorsBardwell-Evans, Sam A.
ContributorsLin, Yu-Shen
Source SetsBoston University
Languageen_US
Detected LanguageEnglish
TypeThesis/Dissertation
RightsAttribution-NonCommercial 4.0 International, http://creativecommons.org/licenses/by-nc/4.0/

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