# 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

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topOno, 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 -

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