ScalingStacks

Proposition 5.9 . [01FU]

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Proposition 5.9.

Let θ\theta be a closed (1,1)(1,1)-form and let 𝒳\mathcal{X} be a SNC model on which θ\theta is determined. Then each θ\theta-psh model function φ∈𝒟⁡(X)\varphi\in\mathcal{D}(X) satisfies:

  • (i)

    φ∘emb𝒳\varphi\circ\emb_{\mathcal{X}} is piecewise affine and convex on each face of Δ𝒳\Delta_{\mathcal{X}};

  • (ii)

    φ≤φ∘p𝒳\varphi\leq\varphi\circ p_{\mathcal{X}} with equality if φ\varphi is determined on 𝒳\mathcal{X}.

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