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引用切替：ﾚｽｱﾝｶｰのみ

>>53
> >>52
> つづき
> 
> Boundary geometry
> Here the vertices of the graph correspond to irreducible components of the nodal curve, the labelling of a vertex is the arithmetic genus of the corresponding component, edges correspond to nodes of the curve and the half-edges correspond to the markings.
> The closure of the locus of curves with a given dual graph in {\displaystyle {\overline {\mathcal {M}}}_{g,n}}\overline {{\mathcal  {M}}}_{{g,n}} is isomorphic to the stack quotient of a product {\displaystyle \prod _{v}{\overline {\mathcal {M}}}_{g_{v},n_{v}}}\prod _{v}\overline {{\mathcal  {M}}}_{{g_{v},n_{v}}} of compactified moduli spaces of curves by a finite group.
> In the product the factor corresponding to a vertex v has genus gv taken from the labelling and number of markings {\displaystyle n_{v}}{\displaystyle n_{v}} equal to the number of outgoing edges and half-edges at v. The total genus g is the sum of the gv plus the number of closed cycles in the graph.
> 
> https://en.wikipedia.org/wiki/Moduli_stack_of_elliptic_curves
> Moduli stack of elliptic curves
> (引用終り)
> 以上

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