Geodesic
Asymptotic behaviour of numerical invariants of algebraic varieties
Journal of the European Mathematical Society, Tome 14 (2012) no. 1, pp. 255-271.

Voir la notice de l'article provenant de la source EMS Press

We show that if the degree of a nonsingular projective variety is high enough, maximization of any of the most important numerical invariants, such as class, Betti number, and any of the Chern or middle Hodge numbers, leads to the same class of extremal varieties. Moreover, asymptotically (say, for varieties whose total Betti number is big enough) the ratio of any two of these invariants tends to a well-defined constant.
DOI : 10.4171/jems/301
Classification : 14-XX, 19-XX, 32-XX, 57-XX
Keywords: Asymptotic bound, Castelnuovo theory, Betti number, Hodge number, Chern number, variety of minimal degree 
@article{JEMS_2012_14_1_a6,
     author = {F. L. Zak},
     title = {Asymptotic behaviour of numerical invariants of algebraic varieties},
     journal = {Journal of the European Mathematical Society},
     pages = {255--271},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2012},
     doi = {10.4171/jems/301},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/301/}
}
TY  - JOUR
AU  - F. L. Zak
TI  - Asymptotic behaviour of numerical invariants of algebraic varieties
JO  - Journal of the European Mathematical Society
PY  - 2012
SP  - 255
EP  - 271
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/301/
DO  - 10.4171/jems/301
ID  - JEMS_2012_14_1_a6
ER  - 
%0 Journal Article
%A F. L. Zak
%T Asymptotic behaviour of numerical invariants of algebraic varieties
%J Journal of the European Mathematical Society
%D 2012
%P 255-271
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/301/
%R 10.4171/jems/301
%F JEMS_2012_14_1_a6
F. L. Zak. Asymptotic behaviour of numerical invariants of algebraic varieties. Journal of the European Mathematical Society, Tome 14 (2012) no. 1, pp. 255-271. doi : 10.4171/jems/301. http://geodesic.mathdoc.fr/articles/10.4171/jems/301/

Cité par Sources :