Holomorphic curves in exploded manifolds regularity

Brett Parker

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


The category of exploded manifolds is an extension of the category of smooth manifolds; for exploded manifolds, some adiabatic limits appear as smooth families. This paper studies the ∂ equation on variations of a given family of curves in an exploded manifold. Roughly, we prove that the ∂ equation on variations of an exploded family of curves behaves as nicely as the ∂ equation on variations of a smooth family of smooth curves, even though exploded families of curves allow the development of normal-crossing or log-smooth singularities. The resulting regularity results are foundational to the author’s construction of Gromov–Witten invariants for exploded manifolds.

Original languageEnglish
Pages (from-to)1621-1690
Number of pages70
JournalGeometry and Topology
Issue number4
Publication statusPublished - 17 Jun 2019


  • Exploded manifolds
  • Gluing analysis
  • Holomorphic curves
  • Regularity of dbar equation

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