Journal article
Deformation Theory of Log Pseudo-holomorphic Curves and Logarithmic Ruan–Tian Perturbations
Peking Mathematical Journal, Vol.8(1), pp.41-142
03/2025
DOI: 10.1007/s42543-023-00069-1
Abstract
In a previous paper (Farajzadeh-Tehrani in Geom Topol 26:989–1075, 2022), for any logarithmic symplectic pair (X, D) of a symplectic manifold X and a simple normal crossings symplectic divisor D, we introduced the notion of log pseudo-holomorphic curve and proved a compactness theorem for the moduli spaces of stable log curves. In this paper, we introduce a natural Fredholm setup for studying the deformation theory of log (and relative) curves. As a result, we obtain a logarithmic analog of the space of Ruan–Tian perturbations for these moduli spaces. For a generic compatible pair of an almost complex structure and a log perturbation term, we prove that the subspace of simple maps in each stratum is cut transversely. Such perturbations enable a geometric construction of Gromov–Witten type invariants for certain semi-positive pairs (X, D) in arbitrary genera. In future works, we will use local perturbations and a gluing theorem to construct log Gromov–Witten invariants of arbitrary such pair (X, D).
Details
- Title: Subtitle
- Deformation Theory of Log Pseudo-holomorphic Curves and Logarithmic Ruan–Tian Perturbations
- Creators
- Mohammad Farajzadeh-Tehrani - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Peking Mathematical Journal, Vol.8(1), pp.41-142
- DOI
- 10.1007/s42543-023-00069-1
- ISSN
- 2096-6075
- eISSN
- 2524-7182
- Grant note
- DOI: 10.13039/100000086, name: Directorate for Mathematical and Physical Sciences, award: DMS-2003340
- Language
- English
- Electronic publication date
- 05/08/2023
- Date published
- 03/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984410796002771
Metrics
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