# Universal tropical structures for curves in exploded manifolds

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For any stable curve $f$ in an exploded manifold, this paper constructs a family of curves $\hat f$ with universal tropical structure which contains $f$. Such a family has the property that any other family of curves containing $f$ is locally a small modification of a family which factors through $\hat f$. As such, families of curves with universal tropical structure play an important role in the analysis of the moduli stack of curves and the construction of Gromov-Witten invariants of exploded manifolds.

Autor: Brett Parker

Fuente: https://archive.org/