Relative Chow stability and optimal weights

Tipler, Carl

doi:10.1090/proc/16426

Relative Chow stability and optimal weights
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by Carl Tipler;

Proc. Amer. Math. Soc. 151 (2023), 4015-4026

DOI: https://doi.org/10.1090/proc/16426

Published electronically: May 19, 2023

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Abstract:

For a polarized Kähler 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 $(X,L)$.

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