# Asymptotic behaviour of numerical invariants of algebraic varieties

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 1, page 255-271
- ISSN: 1435-9855

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topZak, 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 -

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