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

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

2006-03-09

arxiv.org/abs/math/0603237v1

Mathematics

Differential Geometry

Scientific paper

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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