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

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

2010-10-19

arxiv.org/abs/1010.3954v2

Mathematics

Algebraic Geometry

Scientific paper

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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