About J-flow, J-balanced metrics, uniform J-stability and K-stability

Abstract

From the work of Dervan-Keller, 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. Eventually, we discuss the case of Kähler classes that may not be integral over a compact manifold.

23 pages; In honor of Ngaiming Mok's 60th birthday. To appear in Asian J. Math

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