Holomorphic curves in exploded manifolds: Kuranishi structure

2013/01/21 by Brett Parker, Parker, Brett · 3 citations
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1301.4748

openalex publication_date 2013/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Universal tropical structures for curves in exploded manifolds
• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds

Cited by

• Tropical gluing formulae for Gromov-Witten invariants
• On the value of thinking tropically to understand Ionel's GW invariants\n relative normal crossing divisors
• Integral counts of pseudo-holomorphic curves

Related

• Holomorphic curves in exploded manifolds: Compactness
• Exploded Fibrations
• Gromov Witten invariants of exploded manifolds
• Universal tropical structures for curves in exploded manifolds
• Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks: II