ScalingStacks

Theorem 5.2 . [05B4]

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Theorem 5.2.

In the situation of Remark 5.1 let u∈τu\in\tau be a vertex of 𝔇\mathfrak{D} with corresponding irreducible component Y⊆𝔛~′′Y\subseteq\tilde{\mathfrak{X}}^{\prime\prime} as in Corollary 2.9 (f). Let SS be the closed point in the special fibre of 𝔛\mathfrak{X} corresponding to τ\tau. Then

deg(c1(𝒪(h∘p𝔛′))n.Y)=deg(S)⋅n!⋅MA(h)(u).\Deg\left(c_{1}\left(\mathcal{O}(h\circ p_{\mathfrak{X}^{\prime}})\right)^{n}.Y\right)=\Deg(S)\cdot n!\cdot\MA(h)(u).

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