Répartition des spectres logarithmiques de l'énergie à l'équilibre

Huayi Chen (1) , Catriona Maclean (1)

1 IF - Institut Fourier

Let $L$ be a big invertible sheaf on a complex projective variety, equipped with two continuous metrics. We prove that the distribution of the eigenvalues of the transition matrix between the $L^2$ norms on $H^0(X,nL)$ with respect to the two metriques converges as $n$ goes to infinity to a Borel probability measure on $¥mathbb R$. This result can be thought of as a generalization of the existence of the energy at the equilibrium as a limit, or an extension of Berndtsson's results to a more general context of graded linear series. Our approach also permits to obtain a $p$-adic analogue of the result.

Mots clés: faisceaux inversibles; métriques hermitiennes; énergie à l'équilibre; spectre logarithmique; mesure limite

Domaines: Géométrie métrique [math.MG]; Théorie des nombres [math.NT]

Huayi Chen, Catriona Maclean. Répartition des spectres logarithmiques de l'énergie à l'équilibre. 2013. ⟨hal-00816341v1⟩