My understanding of the moduli space of stable log maps comes from a series of three papers: [GSa] [ACGS20] [Sieb] \(X = \mathbb P^1\) with trivial log structure, \(g = 0\), \(n = 0\) References 3 [ACGS20] Abramovich, Chen, Gross, Siebert — Decomposition Of Degenerate Gromov–Witten Invariants (2020) [GSa] Gross, Siebert — Logarithmic Gromov-Witten Invariants [Sieb] Siebert — Punctured Logarithmic Maps | Contents | Ems Press