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

Ono, Hajime; Sano, Yuji; Yotsutani, Naoto

doi:10.5802/aif.2722

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 ¹ ; Sano, Yuji ² ; Yotsutani, Naoto ³

¹ Tokyo University of Science Faculty of Science and Technology Department of Mathematics 2641 Yamazaki, Noda Chiba 278-8510 (Japan)
² Kumamoto University Graduate School of Science and Technology 2-39-1, Kurokami Kumamoto, 860-8555 (Japan)
³ University of Science and Technology of China School of Mathematics Hefei, Anhui 230026 P.R. (China)

Annales de l'Institut Fourier, Tome 62 (2012) no. 4, pp. 1265-1287.

Résumé
Abstract

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 $Aut (V, L)$ 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 $Aut (V, L)$ n’est pas discret.

Donaldson proved that if a polarized manifold $(V, L)$ has constant scalar curvature Kähler metrics in $c_{1} (L)$ and its automorphism group $Aut (V, L)$ 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 $Aut (V, L)$ is not discrete.

MR Zbl | 1 citation dans Numdam

DOI : 10.5802/aif.2722

Classification : 53C55, 53C21, 55N91
Keywords: asymptotic Chow stability, Kähler metric of constant scalar curvature, toric Fano manifold, Futaki invariant
Mot clés : stabilité asymptotique au sens de Chow, métrique kählérienne à courbure scalaire contsante, variété de Fano torique, invariant de Futaki

Affiliations des auteurs :

Ono, Hajime ¹ ; Sano, Yuji ² ; Yotsutani, Naoto ³

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     title = {An example of an asymptotically {Chow} unstable manifold  with constant scalar curvature},
     journal = {Annales de l'Institut Fourier},
     pages = {1265--1287},
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Ono, Hajime; Sano, Yuji; Yotsutani, Naoto. An example of an asymptotically Chow unstable manifold  with constant scalar curvature. Annales de l'Institut Fourier, Tome 62 (2012) no. 4, pp. 1265-1287. doi : 10.5802/aif.2722. http://www.numdam.org/articles/10.5802/aif.2722/

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