Theorem 3.3.1 . [01KD]

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Theorem 3.3.1.

Let $X$ be a projective variety of dimension $n$ over $F$ . Let $\overline{L}$ be an ample line bundle on $X$ with a semi-positive adelic metric such that $e(\overline{L})=({\widehat{c}}_{1}(\overline{L})^{n+1}|X)=0$ . Let $(x_{j})$ be a generic sequence of algebraic point in $X$ such that $h_{\overline{L}}(x_{j})\rightarrow 0$ . Then, for any line bundle $\overline{M}$ on $X$ with an admissible adelic metric,

\lim_{j\rightarrow\infty}h_{\overline{M}}(x_{j})=\frac{({\widehat{c}}_{1}(\overline{L})^{n}{\widehat{c}}_{1}(\overline{M})|X)}{(c_{1}(L)^{n}|X)}.