Seshadri constants and interpolation on commutative algebraic groups
[Constantes de Seshadri et interpolation dans les groupes algébriques commutatifs]
Fischler, Stéphane1 ; Nakamaye, Michael2
1 Univ Paris-Sud Laboratoire de Mathématiques d’Orsay CNRS, F-91405 Orsay (France)
2 Department of Mathematics and Statistics University of New Mexico Albuquerque, New Mexico 87131 (U.S.A.)
Annales de l'Institut Fourier, Tome 64 (2014) no. 3, pp. 1269-1289.

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.

DOI : 10.5802/aif.2880
Classification : 14L10, 14C20, 11J95, 14L40
Keywords: Interpolation estimate, Seshadri constant, ample line bundle, commutative algebraic group, obstruction subgroup, Seshadri exceptional subvariety
Mot clés : lemme d’interpolation, constante de Seshadri, fibré ample, groupe algébrique commutatif, sous-groupe obstructeur, sous-variété exceptionnelle de Seshadri
Fischler, Stéphane 1 ; Nakamaye, Michael 2

1 Univ Paris-Sud Laboratoire de Mathématiques d’Orsay CNRS, F-91405 Orsay (France)
2 Department of Mathematics and Statistics University of New Mexico Albuquerque, New Mexico 87131 (U.S.A.) 
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Fischler, Stéphane; Nakamaye, Michael. Seshadri constants and interpolation on commutative algebraic groups. Annales de l'Institut Fourier, Tome 64 (2014) no. 3, pp. 1269-1289. doi : 10.5802/aif.2880. http://www.numdam.org/articles/10.5802/aif.2880/

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