Fischler, Stéphane; Nakamaye, Michael
Seshadri constants and interpolation on commutative algebraic groups  [ Constantes de Seshadri et interpolation dans les groupes algébriques commutatifs ]
Annales de l'institut Fourier, Tome 64 (2014) no. 3 , p. 1269-1289
MR 3330170 | Zbl 06387307
doi : 10.5802/aif.2880
URL stable : http://www.numdam.org/item?id=AIF_2014__64_3_1269_0

Classification:  14L10,  14C20,  11J95,  14L40
Mots clés: lemme d’interpolation, constante de Seshadri, fibré ample, groupe algébrique commutatif, sous-groupe obstructeur, sous-variété exceptionnelle de Seshadri
Dans cet article on étudie les lemmes d’interpolation dans les compactifications à la Serre de groupes algébriques commutatifs. On obtient un résultat aussi précis que les meilleurs lemmes de multiplicité connus, ce qui améliore notablement le lemme d’interpolation de Masser et celui du premier auteur. Ce raffinement provient d’une approche différente, fondée sur les constantes de Seshadri et les théorèmes d’annulation, et utilise les propriétés particulières des compactifications considérées.
In this article we study interpolation estimates on a special class of compactifications of commutative algebraic groups constructed by Serre. We obtain a large quantitative improvement over previous results due to Masser and the first author and our main result has the same level of accuracy as the best known multiplicity estimates. The improvements come both from using special properties of the compactifications which we consider and from a different approach based upon Seshadri constants and vanishing theorems.

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