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Holomorphic curves in exploded manifolds: Kuranishi structure

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arxiv 1301.4748 v6 pith:ZDKIHTOI submitted 2013-01-21 math.SG

Brett Parker This is my paper · ORCID
classification math.SG
keywords curveskuranishiholomorphicmodulistackstructureexplodedmanifolds
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This paper constructs a Kuranishi structure for the moduli stack of holomorphic curves in exploded manifolds. To avoid some technicalities of abstract Kuranishi structures, we embed our Kuranishi structure inside an ambient moduli stack of not-necessarily-holomorphic curves. The construction also works for the moduli stack of holomorphic curves in any compact symplectic manifold.

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  1. Gromov-Witten invariants of log Calabi-Yau 3-folds are holomorphic lagrangian correspondences

    math.AG 2025-06 conditional novelty 7.0 of 10

    Log Gromov-Witten invariants of Calabi-Yau 3-folds are canonically represented by holomorphic lagrangian cycles in a new Weinstein-style category, with a conjectural unitary bridge to Donaldson-Thomas invariants.

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