English

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

R2 v1 2026-06-21T23:12:34.810Z