Moduli Space Of Pre-Stable Log Curves

\(\mathfrak M(G,\mathbf g) \): is the moduli space of \((G,\mathbf g)\)-marked pre-stable curves over the ground field \(k\) with its basic log structure as a nodal curve.
\(\mathfrak{M}_B(G, \mathbf{g}) \): the base change of \((G, \mathbf g)\)-marked pre-stable curves to a base \(B\).
\(\mathfrak M_B^\circ(G, \mathbf g)\): the stack of \((G, \mathbf g)\)-marked punctured curves over \(B\), admitting negative contact orders at the marked sections.

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