Holomorphic curves in exploded manifolds: Kuranishi structure

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.

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

References in corpus (4)

• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
• Virtual neighborhood technique for pseudo-holomorphic spheres
• Universal tropical structures for curves in exploded manifolds
• Integral counts of pseudo-holomorphic curves

Cited by in corpus (7)

• Decomposition of degenerate Gromov-Witten invariants
• Punctured logarithmic maps
• Tropical gluing formulae for Gromov-Witten invariants
• Gluing formula for Gromov-Witten invariants in a triple product
• On the value of thinking tropically to understand Ionel's GW invariants relative normal crossing divisors
• Notes on exploded manifolds and a tropical gluing formula for Gromov-WItten invariants
• Integral counts of pseudo-holomorphic curves