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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   )   :  =    lim     infP  ∊  Uh  D    (  P  )   →  ∞    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 (nef) or pseudo‐effective.

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