ScalingStacks

Theorem 5.4 . [02ER]

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Theorem 5.4.

Let XX be a projective algebraic manifold of general type whose canonical ring R=⊕n∈ℕH0(X,ωXn)R={\displaystyle\oplus_{n\in\mathbb{N}}}H^{0}(X,\omega_{X}^{n}) is of finite type. Then the canonical model of XX, Xc​a​n:=P​r​o​j​(R)X_{can}:=Proj(R) has only canonical singularities. If N=I​n​d​e​x​(Xc​a​n)N=Index(X_{can}) then ωXc​a​n[N]\omega^{[N]}_{X_{can}} is ample.

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