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.
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.
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
@article{AIF_2014__64_3_1269_0, author = {Fischler, St\'ephane and Nakamaye, Michael}, title = {Seshadri constants and interpolation on commutative algebraic groups}, journal = {Annales de l'Institut Fourier}, pages = {1269--1289}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {3}, year = {2014}, doi = {10.5802/aif.2880}, zbl = {1330.14076}, mrnumber = {3330170}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2880/} }
TY - JOUR AU - Fischler, Stéphane AU - Nakamaye, Michael TI - Seshadri constants and interpolation on commutative algebraic groups JO - Annales de l'Institut Fourier PY - 2014 SP - 1269 EP - 1289 VL - 64 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2880/ DO - 10.5802/aif.2880 LA - en ID - AIF_2014__64_3_1269_0 ER -
%0 Journal Article %A Fischler, Stéphane %A Nakamaye, Michael %T Seshadri constants and interpolation on commutative algebraic groups %J Annales de l'Institut Fourier %D 2014 %P 1269-1289 %V 64 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2880/ %R 10.5802/aif.2880 %G en %F AIF_2014__64_3_1269_0
Fischler, Stéphane; Nakamaye, Michael. Seshadri constants and interpolation on commutative algebraic groups. Annales de l'Institut Fourier, Volume 64 (2014) no. 3, pp. 1269-1289. doi : 10.5802/aif.2880. https://aif.centre-mersenne.org/articles/10.5802/aif.2880/
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