no. 4
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, Hajime1 ; Sano, Yuji2 ; Yotsutani, Naoto3
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.

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.

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

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) 
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     title = {An example of an asymptotically {Chow} unstable manifold  with constant scalar curvature},
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2722/

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