### Abstract

This is an expository paper. We will discuss various formulations of Futaki invariant and its relation to the CM line bundle. We will discuss their connections to the K-energy. We will also include proof for certain known results which may not have been well presented or less accessible in the literature. We always assume that M is a compact Kahler manifold. By a polarization, we mean a positive line bundle L over M, then we call (M, L) a polarized manifold.

Original language | English (US) |
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Title of host publication | Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014 |

Editors | Reiko Miyaoka, Akito Futaki, Weiping Zhang, Zizhou Tang |

Publisher | Springer New York LLC |

Pages | 327-348 |

Number of pages | 22 |

ISBN (Print) | 9784431560197 |

DOIs | |

State | Published - Jan 1 2016 |

Event | 10th Geometry Conference on Friendship between China and Japan, 2014 - Shanghai, China Duration: Sep 7 2014 → Sep 11 2014 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 154 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

Other | 10th Geometry Conference on Friendship between China and Japan, 2014 |
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Country | China |

City | Shanghai |

Period | 9/7/14 → 9/11/14 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Tian, G. (2016). Futaki invariant and CM polarization. In R. Miyaoka, A. Futaki, W. Zhang, & Z. Tang (Eds.),

*Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014*(pp. 327-348). (Springer Proceedings in Mathematics and Statistics; Vol. 154). Springer New York LLC. https://doi.org/10.1007/978-4-431-56021-0_18