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Displaying similar documents to “Local volumes of Cartier divisors over normal algebraic varieties”

Characterization of global Phragmén-Lindelöf conditions for algebraic varieties by limit varieties only

Rüdiger W. Braun, Reinhold Meise, B. A. Taylor (2006)

Annales Polonici Mathematici

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For algebraic surfaces, several global Phragmén-Lindelöf conditions are characterized in terms of conditions on their limit varieties. This shows that the hyperbolicity conditions that appeared in earlier geometric characterizations are redundant. The result is applied to the problem of existence of a continuous linear right inverse for constant coefficient partial differential operators in three variables in Beurling classes of ultradifferentiable functions.

Schubert varieties and representations of Dynkin quivers

Grzegorz Bobiński, Grzegorz Zwara (2002)

Colloquium Mathematicae

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We show that the types of singularities of Schubert varieties in the flag varieties Flagₙ, n ∈ ℕ, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔸. Similarly, we prove that the types of singularities of Schubert varieties in products of Grassmannians Grass(n,a) × Grass(n,b), a, b, n ∈ ℕ, a, b ≤ n, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔻. We also...

Asymptotic behaviour of numerical invariants of algebraic varieties

F. L. Zak (2012)

Journal of the European Mathematical Society

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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.