An example of an asymptotically Chow unstable manifold with constant scalar curvature

[Un exemple de variété à courbure scalaire constante asymptotiquement instable au sens de Chow]

Ono, Hajime ; Sano, Yuji ; Yotsutani, Naoto

Annales de l'Institut Fourier, Tome 62 (2012), p. 1265-1287 / Harvested from Numdam

Résumé

Donaldson a prouvé que, si une variété polarisée $(V, L)$ admet une métrique kählérienne à courbure scalaire constante dans $c_1(L)$, et si son groupe d’automorphismes $\mathrm{Aut} (V, L)$ est discret, alors $(V, L)$ est asymptotiquement stable au sens de Chow. Dans cet article, nous allons montrer un exemple qui implique que le résultat ci-dessus ne s’étend pas au cas où $\mathrm{Aut} (V, L)$ n’est pas discret.

Abstract

Donaldson proved that if a polarized manifold $(V, L)$ has constant scalar curvature Kähler metrics in $c_1(\!L)$ and its automorphism group $\mathrm{Aut}(V\!\!,\!L)$ is discrete, $(V,L)$ is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where $\mathrm{Aut}(V, L)$ is not discrete.

Détail

Publié le : 2012-01-01

MR 3025743 | Zbl 1255.53057

DOI : https://doi.org/10.5802/aif.2722
Classification:  53C55,  53C21,  55N91
Mots clés: stabilité asymptotique au sens de Chow, métrique kählérienne à courbure scalaire contsante, variété de Fano torique, invariant de Futaki

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