Asymptotic behaviour of numerical invariants of algebraic varieties

Zak, F. L.. "Asymptotic behaviour of numerical invariants of algebraic varieties." Journal of the European Mathematical Society 014.1 (2012): 255-271. <http://eudml.org/doc/277692>.

@article{Zak2012,
abstract = {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.},
author = {Zak, F. L.},
journal = {Journal of the European Mathematical Society},
keywords = {asymptotic bound; Castelnuovo theory; Betti number; Hodge number; Chern number; variety of minimal degree; asymptotic bound; Castelnuovo theory; Betti number; Hodge number; Chern number; variety of minimal degree},
language = {eng},
number = {1},
pages = {255-271},
publisher = {European Mathematical Society Publishing House},
title = {Asymptotic behaviour of numerical invariants of algebraic varieties},
url = {http://eudml.org/doc/277692},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Zak, F. L.
TI - Asymptotic behaviour of numerical invariants of algebraic varieties
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 1
SP - 255
EP - 271
AB - 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.
LA - eng
KW - asymptotic bound; Castelnuovo theory; Betti number; Hodge number; Chern number; variety of minimal degree; asymptotic bound; Castelnuovo theory; Betti number; Hodge number; Chern number; variety of minimal degree
UR - http://eudml.org/doc/277692
ER -