Asymptotics of eigensections on toric varieties
Annales de l'Institut Fourier, Volume 63 (2013) no. 2, pp. 733-762.

Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities |ϕ n | 2 =|s N | 2 /||s N || L 2 2 for eigensections s N Γ(X,L N ) approaching a semiclassical ray. Here X is a normal compact toric variety and L is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate and Zelditch.

En utilisant les propriétés d’exhaustion des fonctions plurisousharmoniques invariantes en combinaison avec les données combinatoires basiques des variétés toriques, nous montrons des résultats de convergence pour des suites de densités |ϕ n |=|s N | 2 /||s N || L 2 2 des sections propres s N Γ(X,L N ) approchant un rayon semi-classique. Ici X est une variété torique normale et L désigne un fibré en droites ample muni d’une métriqué positive quelconque invariante par rapport à l’action de la forme compacte du tore. Notre travail était motivé par ceux de Shiffman, Tate et Zelditch et généralise ceux-ci.

Received:
Revised:
Accepted:
DOI: 10.5802/aif.2775
Classification: 34L20,  14M25,  22E70
Keywords: asymptotics of eigensections, toric varieties, plurisubharmonic
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Huckleberry, A.; Sebert, H. Asymptotics of eigensections on toric varieties. Annales de l'Institut Fourier, Volume 63 (2013) no. 2, pp. 733-762. doi : 10.5802/aif.2775. https://aif.centre-mersenne.org/articles/10.5802/aif.2775/

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