We study the tropicalization of the moduli space of algebraic spin curves, \(\overline{\mathcal {S}}_{g,n}\). We exhibit its combinatorial stratification and prove that the strata are irreducible. We construct the moduli space of tropical spin curves \(\overline{S}_{g,n}^{{\text {trop}}}\), prove that is naturally isomorphic to the skeleton of the analytification, \(\overline{S}_{g,n}^{{\text {an}}}\), of \(\overline{\mathcal {S}}_{g,n}\), and give a geometric interpretation of the retraction of \(\overline{S}_{g,n}^{{\text {an}}}\) onto its skeleton in terms of a tropicalization map \(\overline{S}_{g,n}^{{\text {an}}}\rightarrow \overline{S}_{g,n}^{{\text {trop}}}\).

中文翻译：

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使自旋曲线的模空间变热带

我们研究了代数自旋曲线\（\ overline {\ mathcal {S}} _ {g，n} \）的模空间的热带化。我们表现​​出其组合分层，并证明该层是不可约的。我们构造热带自旋曲线\（\ overline {S} _ {g，n} ^ {{\ text {trop}}} \}的模空间，证明它自然地同构于分析骨架\（\上划线{S} _ {G，N} ^ {{\文本{的}}} \），的\（\划线{\ mathcal {S}} _ {G，N} \），和得到的几何解释根据热带化贴图\（\ overline {S} _ {g，n}，\（\ overline {S} _ {g，n} ^ {{\ text {an}}} \\）缩回到其骨架上^ {{\ text {an}}} \ rightarrow \ overline {S} _ {g，n} ^ {{\ text {trop}}} \）。