A New Notion of Defect for Holomorphic Curves and Their Sequences

I. M. Dektyarev

Vladimir State Pedagogical University

Abstract: In this paper, we study transcendental curves in $\mathbb{P}^n$ and also infinite sequences of rational curves using methods of the value distribution theory of holomorphic mappings and, in particular, the notions of Nevanlinna and Valiron defects. In contrast to the classical case, we study the defects of points in $\mathbb{P}^n$ rather than of divisors. It is shown how the main notions of the theory should be changed to make them meaningful in this context. Analogs of the main theorems are proved. It is established that the sets of defective points are sparse in the sense of an adequately introduced Hausdorff $h$-measure.

Keywords: holomorphic curve, degree, defect, Nevanlinna theory, distribution of values.

UDC: 515.16

Received: 12.02.2002

DOI: 10.4213/faa217

 English version: Functional Analysis and Its Applications, 2002, 36:4, 281–289

Bibliographic databases:

• 
• 
• 
•