Canonical Metrics of Commuting Maps
نویسنده
چکیده
Let φ : X → X be a map on an projective variety. It is known that whenever φ∗ : Pic(X) ⊗ R → Pic(X) ⊗ R has an eigenvalue α > 1, we can build a canonical measure, a canonical height and a canonical metric associated to φ. In the present work, we establish the following fact: if two commuting maps φ, ψ : X → X satisfy these conditions, for eigenvalues α and β and the same eigenvector L, then the canonical metric, the canonical measure, and the canonical height associated to both maps, are identical.
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