TL;DR
This paper establishes a correspondence between log geometry and exploded manifolds to compare Gromov-Witten invariants, aiming to facilitate proofs of gluing formulas across different frameworks.
Contribution
It provides a dictionary linking log geometry and exploded manifolds, enabling comparison and potential unification of Gromov-Witten invariants definitions.
Findings
Established a correspondence between log geometry and exploded manifolds.
Suggested an approach to prove gluing formulas for log Gromov-Witten invariants.
Connected different methods of defining Gromov-Witten invariants.
Abstract
Log Gromov-Witten invariants have recently been defined separately by Gross and Siebert and Abramovich and Chen. This paper provides a dictionary between log geometry and holomorphic exploded manifolds in order to compare Gromov-Witten invariants defined using exploded manifolds or log schemes. The gluing formula for Gromov-Witten invariants of exploded manifolds suggests an approach to proving analogous gluing formulas for log Gromov-Witten invariants.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology