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Asymptotic behaviour of numerical invariants of algebraic varieties

F. L. Zak (2012)

Journal of the European Mathematical Society

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.

Bounds for Chern classes of semistable vector bundles on complex projective spaces

Wiera Dobrowolska (1993)

Colloquium Mathematicae

This work concerns bounds for Chern classes of holomorphic semistable and stable vector bundles on n . Non-negative polynomials in Chern classes are constructed for 4-vector bundles on 4 and a generalization of the presented method to r-bundles on n is given. At the end of this paper the construction of bundles from complete intersection is introduced to see how rough the estimates we obtain are.

Classes d'Euler équivariantes et points rationnellement lisses

Alberto Arabia (1998)

Annales de l'institut Fourier

Lorsqu’un tore T agit sur une variété algébrique complexe X munie de la topologie transcendante, nous définissons la classe d’Euler T -équivariante d’un point fixe isolé x X T , qu’il soit lisse ou non. Cette classe est une fraction rationnelle à un nombre fini de variables et lorsque x est rationnellement lisse dans X , c’est un polynôme qui s’identifie canoniquement à la classe d’Euler équivariante usuelle, mais, réciproquement, lorsque la classe d’Euler équivariante est polynomiale, il n’est pas toujours...

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