I read somewhere that if $X$ is a projective variety of general type over a number field $K$, then rational points are an analogue of entire curves $\mathbf{C}\to X^{an}$ (with $X^{an}$ the analytification of $X\_{\mathbf{C}}$ for some $K\to \mathbf C$).


Rational points are algebraic points of degree $1$ on $X$ and they "correspond" to entire curves.


Naive question:


Let $m\geq 2$. What do algebraic points of degree $m$ on $X$ "correspond" to?



If rational points are like entire curves, then what do algebraic points correspond to
Rational points are (kind of) like maps from a *fixed* curve (say P^1) to X.


Algebraic points of degree m are like curves endowed with a map to X and a degree-m map to P^1. 


