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

Hajime Ono[1]; Yuji Sano[2]; Naoto Yotsutani[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 (2012)

  • Volume: 62, Issue: 4, page 1265-1287
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Ono, Hajime, Sano, Yuji, and Yotsutani, Naoto. "An example of an asymptotically Chow unstable manifold with constant scalar curvature." Annales de l’institut Fourier 62.4 (2012): 1265-1287. <http://eudml.org/doc/251142>.

@article{Ono2012,
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.},
affiliation = {Tokyo University of Science Faculty of Science and Technology Department of Mathematics 2641 Yamazaki, Noda Chiba 278-8510 (Japan); Kumamoto University Graduate School of Science and Technology 2-39-1, Kurokami Kumamoto, 860-8555 (Japan); University of Science and Technology of China School of Mathematics Hefei, Anhui 230026 P.R. (China)},
author = {Ono, Hajime, Sano, Yuji, Yotsutani, Naoto},
journal = {Annales de l’institut Fourier},
keywords = {asymptotic Chow stability; Kähler metric of constant scalar curvature; toric Fano manifold; Futaki invariant; Kähler metric of constant scalar curvature, asymptotic Chow stability},
language = {eng},
number = {4},
pages = {1265-1287},
publisher = {Association des Annales de l’institut Fourier},
title = {An example of an asymptotically Chow unstable manifold with constant scalar curvature},
url = {http://eudml.org/doc/251142},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Ono, Hajime
AU - Sano, Yuji
AU - Yotsutani, Naoto
TI - An example of an asymptotically Chow unstable manifold with constant scalar curvature
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 4
SP - 1265
EP - 1287
AB - 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.
LA - eng
KW - asymptotic Chow stability; Kähler metric of constant scalar curvature; toric Fano manifold; Futaki invariant; Kähler metric of constant scalar curvature, asymptotic Chow stability
UR - http://eudml.org/doc/251142
ER -

References

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