Abstract
In this paper we shall prove some of the basic results in the theory of holomorphic curves using the method of negative curvature which has recently been fruitful in the study of equidimensional holomorphic mappings. The eventual goal of the theory is to understand the position of holomorphic curves in general algebraic varieties: and it seemed to us that substantial progress on this problem necessitated finding new proofs of the classical results. To explain this a little better, it may be useful to give a historical sketch of the subject. The classical theory deals with a non-degenerate holomorphic mapping f:C---~P, which we shall call a hofomorphic curve, and in brief outline developed as follows:
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