Relative $K$-stability and modified $K$-energy on toric manifolds

Bin Zhou; Xiaohua Zhu

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arXiv · math/0603237

Relative $K$-stability and modified $K$-energy on toric manifolds

Bin Zhou·Xiaohua Zhu

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Abstract

In this paper, we discuss the relative $K$-stability and the modified $K$-energy associated to the Calabi's extremal metric on toric manifolds. We give a sufficient condition in the sense of convex polytopes associated to toric manifolds for both the relative $K$-stability and the properness of modified $K$-energy. In particular, our results hold for toric Fano manifolds with vanishing Futaki-invariant. We also verify our results on the toric Fano surfaces.

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BibTeX RIS

Bin Zhou, Xiaohua Zhu. 2006-03-09. Relative $K$-stability and modified $K$-energy on toric manifolds. https://arxiv.org/abs/math/0603237

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