About J-flow, J-balanced metrics, uniform J-stability and K-stability
Résumé
From the work of Dervan-Keller [DK15], there exists a quantization of the critical equation for the J-flow. This leads to the notion of J-balanced metrics. We prove that the existence of J-balanced metrics has a purely algebro-geometric characterization in terms of Chow stability, complementing the result of Dervan-Keller. We also obtain various criteria that imply uniform J-stability and uniform K-stability, strengthening the results of Dervan-Keller. Eventually, we discuss the case of Kahler classes that may not be integral over a compact manifold.