Height Inequality for Holomorphic Curves

摘要

Let X/C be a smooth projective variety, then given a complete curve C in X, it isbasic that one may measure its degree with respect to any line bundle on X. In addition, there is an analogous theory for incomplete curves, and for that matter heights of rational points of varieties defined over number fields. We will be principally concerned with the former while making allusions to the latter in the spirit of the 'dictionary' between value distribution theory and Diophantine geometry as one finds it in the work of Vojta.