JournalsjemsVol. 14, No. 1pp. 255–271

Asymptotic behaviour of numerical invariants of algebraic varieties

  • F. L. Zak

    Russian Academy of Sciences, Moscow, Russian Federation
Asymptotic behaviour of numerical invariants of algebraic varieties cover
Download PDF

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.

Cite this article

F. L. Zak, Asymptotic behaviour of numerical invariants of algebraic varieties. J. Eur. Math. Soc. 14 (2012), no. 1, pp. 255–271

DOI 10.4171/JEMS/301