Holomorphic curves in exploded manifolds: Kuranishi structure
Symplectic Geometry
2025-09-10 v6
Abstract
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.
Keywords
Cite
@article{arxiv.1301.4748,
title = {Holomorphic curves in exploded manifolds: Kuranishi structure},
author = {Brett Parker},
journal= {arXiv preprint arXiv:1301.4748},
year = {2025}
}
Comments
123 pages. Version 2 includes the notion of a moduli stack of decorated curves. v3 updates references to arXiv:0902.0087. v4: slightly improved exposition. v5 includes a background section on stacks over the category of exploded manifolds. v6: improved exposition