An example of an asymptotically Chow unstable manifold with constant scalar curvature
Annales de l'Institut Fourier, Volume 62 (2012) no. 4, p. 1265-1287

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.

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.

DOI : https://doi.org/10.5802/aif.2722
Classification:  53C55,  53C21,  55N91
Keywords: asymptotic Chow stability, Kähler metric of constant scalar curvature, toric Fano manifold, Futaki invariant
@article{AIF_2012__62_4_1265_0,
     author = {Ono, Hajime and Sano, Yuji and Yotsutani, Naoto},
     title = {An example of an asymptotically Chow unstable manifold  with constant scalar curvature},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {4},
     year = {2012},
     pages = {1265-1287},
     doi = {10.5802/aif.2722},
     mrnumber = {3025743},
     zbl = {1255.53057},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2012__62_4_1265_0}
}
Ono, Hajime; Sano, Yuji; Yotsutani, Naoto. An example of an asymptotically Chow unstable manifold  with constant scalar curvature. Annales de l'Institut Fourier, Volume 62 (2012) no. 4, pp. 1265-1287. doi : 10.5802/aif.2722. http://www.numdam.org/item/AIF_2012__62_4_1265_0/

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