Geodesic
Asymptotic behaviour of numerical invariants of algebraic varieties
Journal of the European Mathematical Society, Tome 14 (2012) no. 1, pp. 255-271 Cet article a éte moissonné depuis la source EMS Press

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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 
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     author = {F. L. Zak},
     title = {Asymptotic behaviour of numerical invariants of algebraic varieties},
     journal = {Journal of the European Mathematical Society},
     pages = {255--271},
     year = {2012},
     volume = {14},
     number = {1},
     doi = {10.4171/jems/301},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/301/}
}
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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

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