Geodesic
Equidistribution of Divisors for Sequences of Holomorphic Curves
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 3, pp. 17-25 
I. M. Dektyarev. Equidistribution of Divisors for Sequences of Holomorphic Curves. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 3, pp. 17-25. http://geodesic.mathdoc.fr/item/FAA_2000_34_3_a1/
@article{FAA_2000_34_3_a1,
     author = {I. M. Dektyarev},
     title = {Equidistribution of {Divisors} for {Sequences} of {Holomorphic} {Curves}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {17--25},
     year = {2000},
     volume = {34},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2000_34_3_a1/}
}
TY  - JOUR
AU  - I. M. Dektyarev
TI  - Equidistribution of Divisors for Sequences of Holomorphic Curves
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2000
SP  - 17
EP  - 25
VL  - 34
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/FAA_2000_34_3_a1/
LA  - ru
ID  - FAA_2000_34_3_a1
ER  - 
%0 Journal Article
%A I. M. Dektyarev
%T Equidistribution of Divisors for Sequences of Holomorphic Curves
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2000
%P 17-25
%V 34
%N 3
%U http://geodesic.mathdoc.fr/item/FAA_2000_34_3_a1/
%G ru
%F FAA_2000_34_3_a1

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

We study holomorphic curves in an $n$-dimensional complex manifold on which a family of divisors parametrized by an $m$-dimensional compact complex manifold is given. If, for a given sequence of such curves, their areas (in the induced metric) monotonically tend to infinity, then for every divisor one can define a defect characterizing the deviation of the frequency at which this sequence intersects the divisor from the average frequency (over the set of all divisors). It turns out that, as well as in the classical multidimensional case, the set of divisors with positive defect is very rare. (We estimate how rare it is.) Moreover, the defect of almost all divisors belonging to a linear subsystem is equal to the mean value of the defect over the subsystem, and for all divisors in the subsystem (without any exception) the defect is not less than this mean value.

[1] Dektyarev I. M., “Usrednennye defekty golomorfnykh otobrazhenii”, Mnogomernyi kompleksnyi analiz, Izd-vo In-ta fiziki SO AN SSSR, Krasnoyarsk, 1985, 64–77 | MR

[2] Dektyarev I. M., “Ravnoraspredelennost znachenii pri polinomialnykh otobrazheniyakh”, Funkts. analiz i ego pril., 33:4 (1999), 70–73 | DOI | MR | Zbl

[3] Dektyarev I. M., “Zamechanie o strukture mnozhestva defektnykh divizorov”, DAN SSSR, 292:4 (1987), 800–803 | MR | Zbl

[4] Dektyarev I. M., “Emkost i defektnye divizory”, Funkts. analiz i ego pril., 22:1 (1988), 64–65 | MR

[5] Griffits F., Kharris Dzh., Printsipy algebraicheskoi geometrii, Mir, M., 1982 | MR

[6] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | MR | Zbl

[7] Russakovskii A., Sodin M., “Equidistribution for sequences of polynomial mappings”, Indiana Univ. Math. J., 44:3 (1995), 851–882 | DOI | MR

[8] Molzon R., Shiffman B., Sibony N., “Average growth estimates for hyperplane sections of entire analytic sets”, Math. Ann., 257 (1981), 43–59 | DOI | MR | Zbl