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arXiv · 1010.3954

The numerical equivalence relation for height functions and ampleness and nefness criteria for divisors

Chong Gyu Lee
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Abstract

In this paper, we study properties of Weil height functions associated with numerically trivial divisors. It helps us to define the fractional limit of $h_E$ with respect to $h_D$ on $U$, with $D$ ample: \[ \Flim_D(E,U) := \liminf_{\substack{P \in U h_D(P) \rightarrow \infty}}\dfrac{h_E(P)}{h_D(P)}. \] The value of $\Flim_D(E,U)$ contains numerical information about a divisor $E$, enough to determine whether $E$ is ample, numerically effective or pseudo-effective.

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Chong Gyu Lee. 2011-11-26. The numerical equivalence relation for height functions and ampleness and nefness criteria for divisors. https://doi.org/10.1112/blms%2Fbds023

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