Relative Chow stability and optimal weights

Carl Tipler

Relative Chow stability and optimal weights

Differential Geometry 2017-10-17 v2 Algebraic Geometry

Authors: Carl Tipler

Abstract

For a polarized K\"ahler manifold $(X, L)$ , we show the equivalence between relative balanced embeddings introduced by Mabuchi and $\sigma$ -balanced embeddings introduced by Sano, answering a question of Hashimoto. We give a GIT characterization of the existence of a $\sigma$ -balanced embedding, and relate the optimal weight $\sigma$ to the action of $\mathrm{Aut}_0(X,L)$ on the Chow line of $(X, L)$ .

Cite

@article{arxiv.1710.02536,
  title  = {Relative Chow stability and optimal weights},
  author = {Carl Tipler},
  journal= {arXiv preprint arXiv:1710.02536},
  year   = {2017}
}

Comments

11 pages. Minor correction in Section 4.2 on the orthogonal decomposition of Lie algebras

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