Geodesic
A New Notion of Defect for Holomorphic Curves and Their Sequences
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 35-45

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FAA_2002_36_4_a2,
     author = {I. M. Dektyarev},
     title = {A {New} {Notion} of {Defect} for {Holomorphic} {Curves} and {Their} {Sequences}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {35--45},
     publisher = {mathdoc},
     volume = {36},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a2/}
}
TY  - JOUR
AU  - I. M. Dektyarev
TI  - A New Notion of Defect for Holomorphic Curves and Their Sequences
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2002
SP  - 35
EP  - 45
VL  - 36
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a2/
LA  - ru
ID  - FAA_2002_36_4_a2
ER  - 
%0 Journal Article
%A I. M. Dektyarev
%T A New Notion of Defect for Holomorphic Curves and Their Sequences
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2002
%P 35-45
%V 36
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a2/
%G ru
%F FAA_2002_36_4_a2
I. M. Dektyarev. A New Notion of Defect for Holomorphic Curves and Their Sequences. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 35-45. http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a2/